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Name _____________________ Geometry Semester 1 Review Guide 1 2014-2015
1. _______ Jen and Beth are
Hints: (transformation unit)
graphing triangles on this
coordinate grid. Beth graphed her
triangle as shown. Jen must now
graph the reflection of Beth’s
triangle over the x-axis.
A.
B.
C.
D.
2. _______ The pentagon shown is regular
(transformation unit)
and has rotational symmetry.
What is the angle of rotation?
Angle of rotation:
A. 45° B. 72° C. 90°
D. 60°
How many lines of reflection are there?___
where n is number of sides
Number of lines of reflection = n
3. _________ Trapezoid
is drawn on the coordinate
grid.
(transformation unit)If the reflection
If you reflect the trapezoid over the dashed line, what would
line is diagonal, count on the diagonal!
be the new coordinates of
trapezoid
?
A. S’ (-1, -6) W’ (5, 0) I’ (1, 1)
M’ (-2, -2)
B. S’ (-4, -3) W’ (2, 3) I’ (3, -2)
M’ (0, -5)
C. S’ (1, -6) W’ (-5, 0) I’ (5, -3)
M’ (2, -6)
D. S’ (3, 5) W’ (-4, 9) I’ (-3, 5)
M’ (-6, 2)
4. _________ Find the new coordinates of ∆
rotated 90° clockwise about the
origin.
A. M’ (-6, 1) Q’ (-2, 1) H’ (-4, 5)
B. M’ (6, -1) Q’ (2, -1) H’ (4, -5)
C. M’ (5, 4) Q’ (-1, 6) H’ (-2, 1)
D. M’ (8, 7) Q’ (8, 3) H’ (5, 4)
when it is
(transformation unit)
Re-plot on a bigger graph!
5. __________
(transformation unit) *Assume the
rotation is counterclockwise unless
otherwise stated.
A.
Angle of rotation =
where n is
number of sides.
B.
How many turns is in a 270° rotation?
C.
Where will EI end up if you turn the
D.
figure that many counterclockwise?
6. ________
(transformation unit)Angle of rotation =
where n is number of sides.
How many turns is in a 240° rotation?
Where will X end up if you turn the
figure that many counterclockwise?
7. _________ Which of the following is not a rigid
(transformation unit) A rigid
transformation?
transformation occurs when the preimage and
the image are congruent. A rigid transformation
A. Reflection
C. Translation
B. Rotation
D. Dilation
preserves:

Distance (lengths of sides are the same

Angle measure (angles are congruent)

Shape (parallel sides remain parallel,
shape does not change)
8. ________ Will the rotation of a pair of parallel lines always
(transformation unit) A rotation is an
result in another pair of parallel lines?
example of a rigid transformation!
A. yes, they will remain parallel to each other through any rotation
B. Only if the lines are rotated 180° or 360°
C. No, they will always result in intersecting lines
D. Bo, they will always result in perpendicular lines
9. _________ Square ABCD, shown at the right, is translated
(transformation unit) A translation is an
up 3 units and right 2 units to
example of a rigid transformation!!
produce rectangle A’B’C’D’.
Which statement is true?
A
∥ ′ ′ and
B
′ ′ and
′ ′
′ ′ and 3
C
2
D
2
∥ ′ ′
′ ′ and
′ ′
3
′ ′
10. __________What would be the image point B after a
(transformation unit) The line y = 2 is a
reflection over the line y = 2 and a translation
4 units right and 2 units down?
y
A. (1, 4)
B. (11, -4)
C. (1, -4)
D. (1, 0)
horizontal line through 2 on the y-axis.
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-1
-2
B
-3
-4
-5
-6
x
12. ___________ Steve created this design for a wall mural.
(transformation unit) Choose one of the
three vertices in figure 1, and count to find
its corresponding vertex in image 2.
Which describes the translation from figure 1 to figure 2?
A. up 3 units and right 1 unit
units
B. down 1 unit and left 3 units
units
C. up 4 units and right 4
D. down 4 units and left 4
13. _________Given: Quadrilateral ABCD
on this graph.
Which graph shows the reflection of
ABCD over line l?
A.
C.
B.
D.
(transformation unit) Use patty paper
(transformation unit) Example of dilation:
14. ________ Which description MOST accurately describes a
dilation?
A. When a shape is dilated, the parallel lines remain parallel
B. When a shape is dilated, the angles within the shape change
C. When a shape is dilated, the orientation of the shape
changes
D. When a shape is dilated, the distance between the lines
stays the same.
15. __________ Mary Ann drew two lines on the chalkboard.
Her two lines lie in the same plane but share no common points.
Which could be a description of Mary Ann’s drawing?
A. A set of skew lines
C. A set of adjacent rays
B. A set of parallel lines
D. A set of collinear points
16. _________ Lines
the
and
are parallel. The
, and
(Language of Geometry)
(Language of Geometry)
.
Which statement explains why you can use the equation
to solve for
?
Corresponding example: ∠1 & ∠5
A. Alternate Exterior Angles are congruent
Alternate Interior example: ∠3 & ∠6
B. Alternate Interior Angles are congruent
Alternate Exterior example: ∠1 & ∠8
C. Complementary Angles are congruent
D. Corresponding Angles are congruent
17. _________ Greg used a compass and straight edge to draw the
construction below.
(Triangles) Vocab:
Concurrent: meet at a point
Which of these is shown by this
construction?
Median: line from the vertex of a
triangle to midpoint of opposite side
Altitide: line starting from the vertex
of a triangle and creating a right angle
with the opposite side (height)
A. The medians of a triangle are concurrent
B. The altitudes of a triangle are concurrent
C. The angle bisectors of a triangle are concurrent
D. The perpendicular bisectors of a triangle are concurrent
Angle bisector: line that divides an
angle into two congruent parts
Perpendicular bisector: line that may or
may not start at the vertex, but goes to
the midpoint of the opposite side at a
right angle.
18. ____________ A segment has endpoints (-4, 8) and (3, -2).
What are the coordinates of the midpoint?
A. (-3.5, 6)
C. (-0.5, 3)
B. (-1, 6)
D. (-1.5, 3)
19. _____________ line Q is perpendicular to the line for the
equation:
,
)
(Language of Geometry)
Perpendicular lines have opposite
What is the slope of line Q?
B. -
(
Parallel lines have the same slope.
y=- x–4
A.
(Language of Geometry)
C. D.
reciprocal slopes.
20. ________
(Quadrilaterals)
Points P, Q, and R are shown below. If these points are all vertices
of a parallelogram then which point would represent the
coordinates of the fourth vertex of parallelogram PRQS.
In a parallelogram, opposide sides are
P
A
(4,6)
B
(8,-1)
C
(5,2)
D
(9,1)
parallel. Use slope to help find the last
point.
R
Q
21. ___________ What is the coordinate of the midpoint of
?
(Language of Geometry)
Where is the middle of -4 and 2?
A. -2
B. -1
C. 3
D. 6
22. __________ Which of the following is unneccessary to prove
that the 2 base angles of an isosceles triangle are congruent?
A. The angle sum theorem for triangles
B. SAS postulate
C. The definition of angle bisector
D. The definition of congruent triangles
(Triangles) Isosceles triangles:
23. __________ What is the perimeter of the triangle?
(Language of Geometry)
A. 18
Perimeter = add up all sides
B. 20
Use pythagorean theorem to find the
side lengths.
C. 52
D. 134
24. __________ Square EFGH is shown below. A dilation of 2
centered at (2,2) is performed.
The resulting square is
The center is the fixed point. The
other vertices will be twice as far from
labeled E’F’G’H’.
What is the length of
(Transformatons)
(2, 2)
′ ′?
A. 2 units
B. 3 units
C. 5 units
D. 6 units
25. __________ Which of the following is necessary to prove
∠3 is exterior angle. ∠1 and
that a triangle’s exterior angle equals the sum of the two
∠2 are
remote interior angles?
remote
A. the definition of complementary angles
B. The definition of angle bisector
C. The definition of supplementary angles
D. The definition of congruent triangles
interior
angles
26. _________ A segment connects the midpoints on two
sides of a triangle. What is true about this segment (the
midsegment)?
(Triangles )
is a midsegment
=
A. it is always horizontal and half the length of each side.
B. It is always perpendicular to the two sides it joins and
forms an isosceles triangle with the portions of the sides above
it.
C. It is always parallel to the third side and half the as long as
the third side.
D. It is always half the length of those two sides and parallel
to the third.
27. _________ When proving the exterior angle sum theorem,
(Triangles) The polygon exterior angle
the first step is to show that an exterior angle of a polygon and
theorem: the sum of the exterior angles
an interior angle of a polyhon add together to equal 180°.
of any polygon = 360
Which angle classification justifies this step?
A. Vertical angles
B. Corresponding angles
C. Complementary angles
D. Linear Pairs of angles
28. __________ and
of
and
are the midpoints
, respectively.
is the midsegment! See #26
What does the midpoint theorem tell us
about the relationship between
(Triangles)
and
?
A.
is ½ the length of
B.
is twice the length of
C.
and
are not related by that theorem
D.
and
are equal in length
29. __________ Which diagram shows a triangle
drawn so that it is congruent to
A.
B.
?
similar?
A. 30°
B. 60°
C. 90°
D. 70°
size/measure. Use patty paper if
necessary.
C.
D.
30. __________ In the diagram below, what is the measure
of ∠ if the triangles ∆
(Triangles) Congruent means equal in
and ∆
are
(Triangles)
**In similar triangles, corresponding
angles are congruent!
31. ____________ Triangle
is rotated to become triangle
. Without the use of any measurement devices,
which could be used to prove that triangle
is congruent to
triangle
?
(Triangles)
You must have 3 pairs of congruent
angles and sides to use ASA or SAS.
A. SAS beause both are
The sides and angles must be
right triangles, JK is
corresponding!!
congruent to J’K’ and KL is
Try highlighting the information in the
congruent to K’L’
multiple choices to see if the sides and
B. ASA because both are
angles correspond.
right triangles and JL is
congruent to J’L’
C. SAS because both are
right triangles, JL is congruent to J’L’ and JK is congruent to K’L’
D. ASA because both are right triangles and angle J is congruent
to angle L’ and JK is conguent to K’L’
32. _________ Triangle
is rotated, reflected, and
translated to yield
triangle
Be careful on the order of the sides and
.
angles!
Which statement proves
that the two triangles are
congruent?
A.
and
is taken to
is taken to
,
B.
is taken to
, and
C.
is taken to
,
is taken to
, and
is taken to
is taken to
,
is taken to
, and
is taken to
.
is taken to
.
.
D.
.
(Triangles)
33. ___________ Which of the triangles below is similar to
ΔXYZ?
(Triangles)
In similar figures, sides are
proportional. Write pairs of
corresponding sides as fractions and
simplify. If they all reduce to the same
number, this is the similarity ratio. If
they do nt all reduce to the same
number, the triangles are not similar.
Be careful when you write the
A.
C.
corresponding sides as fractions – be
consistant on which triangle is the
numerator and which is the denominator!
B.
D. all of the above
34. _________ Which statement correctly completes
the sentence below?
(Triangles)
There is no AAA congruence
theorem!
If two distinct pairs of angles in two triangles are
congruent, then _________
A. The pair of included sides must also be congruent and
the triangles must be congruent
B. The pair of included sides must also be congruent and
the triangles must be similar
C. The third pair of angles must also be congruent and the
triangles must be congruent
D. The third pair of angles must also be congruent and the
triangles must be similar.
35. ________ The dotted lines in the figure below show
how Jenny inscribed circle
in right triangle
on a practice test.
What should Jenny have done differently to answer the question
correctly?
A. Jenny could have used the
(Triangles) Vocab:

the polygon



the incenter.
D. Jenny should have put points A, B, and C at the midpoints of the
triangle.
Angle bisectors are concurrent
at incenter

Perpendicular bisectors are
concurrent at circumcenter
circumscribed.
C. Jenny should have used the bisectors of angles X, Y, and Z to find
Medians are concurrent at
centroid
B. Jenny should have constructed
an inscribed circle. Circle O is
Circumcircle/circumscribed
circle: around the polygon
altitudes of the triangle to find
the incenter.
Incircle/inscribed circle: inside

Altitudes are concurrent at
orthocenter
36. _________ Solve for x and y:
A. x = 99 y = 74
B. x = 74 y = 99
(Quadrilaterals) If a
quadrilateral is inscribed in a
circle, then opposite angles are
supplementary:
C. x = 81 y = 106
D. x = 106 y = 81
37. ____________ True or false: If a figure is a
parallelogram then it is a rectnagle.
38. __________ Which of the following quadrilaterals DOES
(Quadrilaterals)
NOT have perpendicular diagonals?
A. rhombus
B. square
C. kite
D. parallelogram
39. __________ Which of the following have congruent
(Quadrilaterals)
diagonals?
Draw the figures
A. rectangle, rhombus, square
B. rectangle, square, isosceles trapezoid
C. kite, parallelogram, trapezoid
D. parallelogram, rectangle, rhombus, square
40. ___________ What are the coordinates of G?
(Quadrilaterals)
A. (2a, b)
B. (-2a, -b)
C. (2a, -b)
D. (-2a, b)
41. _________ The translation vector 〈 8, 12〉 means to go:
A. left 8 down 12
B. right 8 down 12
(Transformations)
〈 , 〉
X is the horizontal slide
Y is the vertical slide
C. left 8 up 12
D. right 8 up 12
42. _________ What is the line of reflection?
A. x = -2
B. x –axis
C. y = -2
D. y- axis
(Transformations)
Hoy Vux
Horizontal lines are of the form
y=k
Vertical lines are of the form
x=h
43. ________Which is the correct list of undefined terms in
(Language of Geometry)
geometry?
A. point, line, ray
B. point, line, plane
C. segment, angle, point
D. plane, helicopter, jet
44. _________ Line A passes through (-3, 5) and (1, -3).
(Language of Geometry) Parallel lines have
What is the slope of the line that is parallel to line A?
the same slope.
A. 2
Perpendicular lines have opposite reciprocal
C. -2
slopes.
Graph the points and count
B.
D. -
or use the
formula
45. _________ Line A passes through (2, 5) and (-1, 1). What
(Language of Geometry) Parallel lines have
is the slope of the line that is perpendicular to line A?
the same slope.
A.
C. -
B.
D. -
Perpendicular lines have opposite reciprocal
slopes.
Graph the points and count
formula
or use the
2014-2015 UCS Geometry
SEMESTER 1 REVIEW GUIDE #2
1.
The following picture is a reflection of the image and
over what line?
2.
Rotate the figure 90°
3.
How many reflection lines exist
to take the octagon onto itself?
preimage
4.
For a circus act, a trapeze artist swings along
the path shown in the coordinate grid. Next,
the trapeze artist swings along the same
path, but 12 feet higher from the original
starting point.
A
C
B
D
5.
Terry made this quilt with the pattern shown.
Which transformations best describe the
relationship between block A and block B ?
A
Two flips
C
A flip and a slide
B
Two slides
D
None of the above
6.
7.
Which transformation, when performed
individually, would transform the rectangle
below onto itself?
A
A clockwise rotation 180° about the
origin
C
A reflection across the x-axis, followed
by a translation up 5 units
B
A clockwise rotation 180° about the
point 7, 3
D
A reflection across the y-axis, followed
by a translation left 12 units
. Look at figure
and its image,
.
Which best describes the series of transformations that were performed on figure
A
a rotation of
units down
B
a reflection across the y-axis and a
translation of units down
and a translation of
?
C
a reflection across the y-axis and a
reflection across the x-axis
D
a rotation of
translation of
counterclockwise and a
units to the right
8.
The “F” below is going to be translated 4 units down and 3 units to the right and then
translated 2 units up and 1 unit to the right.
y
Which of the following single transformations
would have the same effect on the “F” as
performing both of the transformations
listed above?
6
5
4
3
2
1
A
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-1
-2
-3
-4
-5
-6
Translating the “F” 2 units down and 4 units to the right
B
Translating the “F” 6 units down and 2 units to the right
C
Rotating the “F” 180 counterclockwise about the origin
D
Reflecting the “F” over the x-axis
9.
The point (2, 3) is reflected over the x-axis and then translated 4 units to the left and 2
units up. What are the new coordinates of the point?
x
10. Paul and Janelle are getting ready to play a board game. Paul sets up his pieces as shown
in this diagram.
Janelle’s pieces will be set up the same way but
reflected across the line
5 . Which of these
coordinates represents one of Janelle’s pieces?
A
C
(9,10)
D
(7,6)
(4,7)
B
(3,8)
11. Rectangle KLMN is shown below.
If KLMN undergoes a dilation of 2 centered on the
origin to produce K’L’M’N’, which statement is
correct?
A
The equation of the line passing through points N and K is the same as the equation
of the line passing through N’ and K’.
B
The equation of the line passing through points M and N is the same as the equation
of the line passing through M’ and N’.
C
The equation of the line passing through points L and M is the same as the equation
of the line passing through L’ and M’.
D
The equation of the line passing through points K and L is the same as the equation
of the line passing through K’ and L’.
12. Pentagon PENTA undergoes a dilation of 2.5 to produce pentagon P’E’N’T’A’. Which ratio
to the length of ′ ′ ?
is equivalent to the ratio of the length of
13. Which terms does NOT have a formal geometric definition?
A Angle
C
Plane
B Segment
D
Triangle
14. Lines q and r are parallel.
The measure of ∠8 67° and the
measure of ∠2 21
.
Why can you use the equation
67 21
to solve for ?
15. What is the first step in constructing a line segment perpendicular to line segment AB that
passes through the point P as shown below?
•P
A B
16. Construct an equilateral triangle inscribed in a circle.
17. Find the equation of the line passing through the point (–3,–4) and is parallel to the line
8.
having the equation: y =
18. Write an equation for line t can be written as
8
. Perpendicular to line t is line
u, which passes through the point (-8,1). What is the equation of line u?
19. What is the midpoint of
if the coordinate of
A is (3, -4) and the coordinate of B is (-7, 10)? 20. In a triangle with coordinates (1, 4), (2, 8), and (5, 4), what would be the perimeter
rounded to the nearest hundredth?
21. How could a student determine that a triangle and its transformed image are congruent?
A
They are congruent if and only if the triangles are right triangles.
B
They are congruent if and only if the transformed figure was not rotated.
C
They are congruent if and only if corresponding pairs of sides and corresponding
pairs of angles are congruent.
D
They are congruent if and only if corresponding pairs of sides are similar and
corresponding pairs of angles are similar.
22. Which translation from solid-lined figure to dashed-lined figure is 3 units left and 3 units
up? Careful, the units are by 2’s.
23.
A
C
B
D
24.
is reflected across the y-axis.
Which set of congruence statements
explains why the triangles are congruent?
A
and
B
and
C
;
D
;
;
: SAS
;
;
: ASA
: SSS
;
: AAA
25.
What is necessary to prove that a triangle's exterior angle equals the sum of the two
remote interior angles?
26.
Two frame houses are built, a taller one next to a shorter one. If the frame houses are
to be similar in their construction, what should the dimensions of the bigger house be?
27. Which steps correctly state how to construct the circumscribed circle of a triangle?
A
To find the center of the circumscribed circle, find the point of concurrence of the
three internal angle bisectors. The radius of the circle is the segment that joins the
center and one side of the triangle and is perpendicular to the side.
B
To find the center of the circumscribed circle, find the point of concurrence of the
three medians of the triangle. The radius of the circle is the segment that joins the
center and one of the vertices of the triangle.
C
To find the center of the circumscribed circle, find the point of concurrence of the
three altitudes. The radius of the circle is the segment that joins the center and
one of the vertices of the triangle.
D
To find the center of the circumscribed circle, find the point of concurrence of the
three perpendicular bisectors. The radius of the circle is the segment that joins the
center and one of the vertices of the triangle.
28. Which of the other triangles is similar to ΔABC and why?
A
C
B
D
None of the above
29. A dilation with a scale factor of 2 is applied to ∆
to produce ∆ ′ ′ ′ . If measure of ∠
and the measure of ∠
102° what are the measures of ∠ , ∠ ,
∠ ?
30. ∆
is a right triangle. CH is a perpendicular bisector that
goes from vertex C to the hypotenuse AB of the triangle.
How many similar triangles are there?
35°
31. Find the missing side lengths of BC and DC if ∆
~∆
B E 27.5
11 A 26 C
D
32.
Quadrilateral ABCD is inscribed circle O
What is true about ∠ and ∠ ?
33.
135° What is the measure of ∠
42.5
in the diagram above?
F
34. Mrs. Douglas drew a quadrilateral on the chalkboard. She wanted her class to prove
it was a rectangle. What conditions must be met for the quadrilateral to be a rectangle?
35. What is the perimeter of the triangle shown below?
36. Jeremywasgiven
,shownbelow.
ShowhowJeremycouldconstructtheperpendicularbisectorof .
Explaineachstep.
 DescribehowJeremycoulddrawtheperpendicularbisectorof .
 DescribehowJeremycouldsketchtheperpendicularbisectorof .
Usewords,numbers,and/orpicturestoshowyourwork.Writeyour
answer(s)onthepaperprovided.

37. Solve for a, x, and b: Name _____________________ Geometry Semester 1 Review Guide 1 2014-2015
1. _______ Jen and Beth are graphing
Hints: (transformation unit)
triangles on this coordinate grid. Beth
graphed her triangle as shown. Jen
must now graph the reflection of
Beth’s triangle over the x-axis.
A.
B.
C.
D.
2. _______ The pentagon shown is regular and
(transformation unit)
has rotational symmetry.
What is the angle of rotation?
Angle of rotation:
A. 45° B. 72° C. 90°
D. 60°
How many lines of reflection are there?______
where n is number of ways it
could look the same
3. _________ Trapezoid
is drawn on the coordinate grid.
(transformation unit)
If you reflect the trapezoid over the dashed line, what would be the
If the reflection line is diagonal,
new coordinates of trapezoid
count on the diagonal!
A.
B.
C.
D.
S’ (-1, -6) W’ (5, 0)
S’ (-4, -3) W’ (2, 3)
S’ (1, -6) W’ (-5, 0)
S’ (3, 5) W’ (-4, 9)
?
I’ (1, 1) M’ (-2, -2)
I’ (3, -2) M’ (0, -5)
I’ (5, -3) M’ (2, -6)
I’ (-3, 5) M’ (-6, 2)
4. _________ Find the new coordinates of ∆
when it is rotated
90° clockwise about the origin.
(transformation unit)
Re-plot on a bigger graph!
A. M’ (-6, 1) Q’ (-2, 1) H’ (-4, 5)
B. M’ (6, -1) Q’ (2, -1) H’ (4, -5)
C. M’ (5, 4) Q’ (-1, 6) H’ (-2, 1)
D. M’ (8, 7) Q’ (8, 3) H’ (5, 4)
5. __________ Regular octagon EIGHTSUP is divided into eight
congruent triangles. Find the image of each point or segment for the
given rotation.
(transformation unit) *Assume
the rotation is counterclockwise
unless otherwise stated.
A.
B.
C.
D.
Angle of rotation =
6. ________ Name the image of X for a 240⁰ counterclockwise
rotation about the center of the regular hexagon.
A. A
B. G
C. O
(transformation unit)
Angle of rotation =
D. H
7. _________ Which of the following is not a rigid transformation?
A. Reflection
C. Translation
(transformation unit) A rigid
transformation occurs when the preimage
and the image are congruent. A rigid
transformation preserves:
B. Rotation
D. Dilation

Distance (lengths of sides are
the same

Angle measure (angles are
congruent)

Shape (parallel sides remain
parallel, shape does not change)
8. ________ Will the rotation of a pair of parallel lines always result
(transformation unit)
in another pair of parallel lines?
A. yes, they will remain parallel to each other through any rotation
B. Only if the lines are rotated 180° or 360°
C. No, they will always result in intersecting lines
D. No, they will always result in perpendicular lines
9. _________ Square ABCD, shown at the right, is translated up
3 units and right 2 units to produce rectangle A’B’C’D’.
Which statement is true?
A
∥ ′ ′ and
B
′ ′ and
′ ′
′ ′ and 3
C
D
2
2
∥ ′ ′
′ ′ and
′ ′
3
′ ′
(transformation unit)
10. __________What would be the image point B after a
reflection over the line y = 2 and a translation
4 units right and 2 units down?
The line y = 2 is a horizontal line
through 2 on the y-axis.
y
6
5
4
3
2
1
A. (1, 4)
B. (11, -4)
C. (1, -4)
D. (1, 0)
(transformation unit)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-1
-2
B
-3
-4
-5
-6
x
11. ___________ Steve created this design for a wall mural.
Which describes the translation from figure 1 to figure 2?
A.
B.
C.
D.
up 3 units and right 1 unit
down 1 unit and left 3 units
up 4 units and right 4 units
down 4 units and left 4 units
12. ________ Which description MOST accurately describes a
dilation?
A. When a shape is dilated, the parallel lines remain parallel
B. When a shape is dilated, the angles within the shape change
C. When a shape is dilated, the orientation of the shape changes
D. When a shape is dilated, the distance between the lines stays the
same.
(transformation unit) Choose one
of the three vertices in figure 1, and
count to find its corresponding
vertex in image 2.
(transformation unit) Example of
dilation:
13. _________Given: Quadrilateral ABCD on
this graph.
(transformation unit) Use patty
paper
Which graph shows the reflection of ABCD over
line l?
A.
C.
B.
D.
14. _________ Lines
the
and
are parallel. The
(Language of Geometry)
, and
.
Corresponding: Same place
Alternate Interior: Z shaped,
interior angles
Alternate Exterior: Z shaped,
exterior angles
Which statement explains why you can use the equation 77
solve for x ?
A. Alternate Exterior Angles are congruent
B. Alternate Interior Angles are congruent
C. Complementary Angles are congruent
D. Corresponding Angles are congruent
25
to
Complementary: Add up to 90
15. __________ Mary Ann drew two lines on the chalkboard. Her
two lines lie in the same plane but share no common points. Which
could be a description of Mary Ann’s drawing?
A. A set of skew lines
C. A set of adjacent rays
B. A set of parallel lines
D. A set of collinear points
16. _________ Greg used a compass and straight edge to draw the
construction below.
(Language of Geometry)
(Triangles) Vocab:
Concurrent: meet at a point
Median: line from the vertex of a
Which of these is shown by this
construction?
triangle to midpoint of opposite side
Altitide: line starting from the
vertex of a triangle and creating a
right angle with the opposite side
(height)
A. The medians of a triangle are concurrent
B. The altitudes of a triangle are concurrent
C. The angle bisectors of a triangle are concurrent
D. The perpendicular bisectors of a triangle are concurrent
17. ____________ A segment has endpoints (-4, 8) and (3, -2). What are
the coordinates of the midpoint?
C. (-0.5, 3)
B. (-1, 6)
D. (-1.5, 3)
18. _____________ line Q is perpendicular to the line for the equation:
y=- x–4
What is the slope of line Q?
B. -
angle into two congruent parts
Perpendicular bisector: line that may
or may not start at the vertex, but
goes to the midpoint of the opposite
side at a right angle.
(Language of Geometry)
(
A. (-3.5, 6)
A.
Angle bisector: line that divides an
C. D.
,
)
(Language of Geometry)
Parallel lines have the same slope.
Perpendicular lines have opposite
reciprocal slopes.
19. ________
(Quadrilaterals)
Points P, Q, and R are shown below. If these points are all vertices of
a parallelogram then which point would represent the coordinates of
the fourth vertex of parallelogram PRQS.
In a parallelogram, opposide sides
A
(4,6)
B
(8,-1)
C
(5,2)
D
(9,1)
20. ___________ What is the coordinate of the midpoint of
?
are parallel. Use slope to help
find the last point.
(Language of Geometry)
Where is the middle of -4 and 2?
A. -2
B. -1
C. 3
D. 6
21. __________ Which of the following is unneccessary to prove
that the 2 base angles of an isosceles triangle are congruent?
A. The angle sum theorem for triangles
B. SAS postulate
C. The definition of angle bisector
D. The definition of congruent triangles
(Triangles) Isosceles triangles:
22. __________ What is the perimeter of the triangle?
(Language of Geometry)
Perimeter = add up all sides
A. 18
B. 20
C. 52
D. 134
23. __________ Square EFGH is shown below. A dilation of 2
centered at (2,2) is performed. The resulting square is
labeled E’F’G’H’.
What is the length of
(Transformatons)
The center is the fixed point.
The other vertices will be twice
′ ′?
as far from (2, 2)
A. 2 units
B. 3 units
C. 5 units
D. 6 units
24. __________ Which of the following is necessary to prove that a
∠3 is exterior angle.
triangle’s exterior angle equals the sum of the two remote interior
∠1 and ∠2 are remote interior
angles?
angles
A. the definition of complementary angles
B. The definition of angle bisector
C. The definition of supplementary angles
D. The definition of congruent triangles
25. _________ A segment connects the midpoints on two sides of a
(Triangles )
triangle. What is true about this segment (the midsegment)?
A. it is always horizontal and half the length of each side.
B. It is always perpendicular to the two sides it joins and forms an
isosceles triangle with the portions of the sides above it.
C. It is always parallel to the third side and half the as long as the
third side.
D. It is always half the length of those two sides and parallel to the
third.
26. _________ When proving the exterior angle sum theorem, the
(Triangles) The polygon exterior
first step is to show that an exterior angle of a polygon and an
angle theorem: the sum of the
interior angle of a polyhon add together to equal 180°. Which angle
exterior angles of any polygon =
classification justifies this step?
360
A. Vertical angles
B. Corresponding angles
C. Complementary angles
D. Linear Pairs of angles
27. __________ R and
are the midpoints of
and
,
respectively.
is the midsegment
What does the midpoint theorem tell us about the relationship
between
(Triangles)
and
?
A.
is ½ the length of
B.
is twice the length of
C.
and
are not related by that theorem
D.
and
are equal in length
28. __________ Which diagram shows a triangle
drawn so that it is congruent to
A.
?
B. 60°
C. 90°
D. 70°
if necessary.
D.
29. __________ In the diagram below, what is the measure of ∠ if
A. 30°
in size/measure. Use patty paper
C.
B.
the triangles ∆
(Triangles) Congruent means equal
and ∆
are similar?
(Triangles)
**In similar triangles,
corresponding angles are
congruent!
30. ____________ Triangle
is rotated to become triangle
.
Without the use of any measurement devices,
which could be used to prove that triangle
is congruent to triangle
?
(Triangles)
You must have 3 pairs of
congruent angles and sides to use
ASA or SAS.
A. SAS beause both are right
triangles, JK is congruent to J’K’ and
The sides and angles must be
KL is congruent to K’L’
corresponding!!
B. ASA because both are right
Try highlighting the information
triangles and JL is congruent to J’L’
in the multiple choices to see if
the sides and angles correspond.
C. SAS because both are right
triangles, JL is congruent to J’L’ and
JK is congruent to K’L’
D. ASA because both are right triangles and angle J is congruent to
angle L’ and JK is conguent to K’L’
31. _________ Triangle
yield triangle
is rotated, reflected, and translated to
.
Be careful on the order of the
Which statement proves
sides and angles!
that the two triangles are
congruent?
A.
is taken to
is taken to
.
(Triangles)
, and
B.
is taken to
, and
is taken to
.
C.
is taken to
,
is taken to
, and
is taken to
D.
is taken to
,
is taken to
, and
is taken to
.
.
32. ___________ Which of the triangles below is similar to
ΔXYZ?
(Triangles)
In similar figures, sides are
proportional. Write pairs of
corresponding sides as fractions
and simplify. If they all reduce
to the same number, this is the
similarity ratio. If they do nt all
reduce to the same number, the
triangles are not similar.
A.
C.
Be careful when you write the
corresponding sides as fractions –
be consistant on which triangle is
the numerator and which is the
denominator!
B.
D. all of the above
33. _________ Which statement correctly completes the
sentence below?
(Triangles)
If two distinct pairs of angles in two triangles are congruent,
then _________
theorem!
There is no AAA congruence
A. The pair of included sides must also be congruent and the
triangles must be congruent
B. The pair of included sides must also be congruent and the
triangles must be similar
C. The third pair of angles must also be congruent and the
triangles must be congruent
D. The third pair of angles must also be congruent and the
triangles must be similar.
34. ________ The dotted lines in the figure below show
how Jenny inscribed circle
in right triangle
on a practice test.
(Triangles) Vocab:

What should Jenny have done differently to answer the question correctly?
A. Jenny could have used the
inside the polygon

B. Jenny should have constructed an
inscribed circle. Circle O is
circumscribed.
C. Jenny should have used the bisectors of angles X, Y, and Z to find the
polygon

Medians are concurrent at
centroid

Angle bisectors are
concurrent at incenter

incenter.
D. Jenny should have put points A, B, and C at the midpoints of the triangle.
Circumcircle/circumscribe
d circle: around the
altitudes of the triangle to find the
incenter.
Incircle/inscribed circle:
Perpendicular bisectors
are concurrent at
circumcenter

Altitudes are concurrent
at orthocenter
35. _________ Solve for x and y:
A. x = 99 y = 74
B. x = 74 y = 99
(Quadrilaterals) If a
quadrilateral is inscribed in a
circle, then opposite angles are
supplementary:
C. x = 81 y = 106
D. x = 106 y = 81
36. ____________ True or false: If a figure is a parallelogram then
it is a rectangle.
37. __________ Which of the following quadrilaterals DOES NOT
have perpendicular diagonals?
A. rhombus
(Quadrilaterals)
Draw the figures and their
diagonals
B. square
C. kite
D. parallelogram
38. __________ Which of the following have congruent diagonals?
(Quadrilaterals)
A. rectangle, rhombus, square
Draw the figures
B. rectangle, square, isosceles trapezoid
C. kite, parallelogram, trapezoid
D. parallelogram, rectangle, rhombus, square
39. _________ The translation vector 〈 8, 12〉 means to go:
(Transformations)
〈 , 〉
A. left 8 down 12
X is the horizontal slide
B. right 8 down 12
Y is the vertical slide
C. left 8 up 12
D. right 8 up 12
40. _________ What is the line of reflection?
(Transformations)
A. x = -2
Horizontal lines: y = #
B. x –axis
Vertical lines: x = #
C. y = -2
D. y- axis
41. ________Which is the correct list of undefined terms in
(Language of Geometry)
geometry?
A. point, line, ray
B. point, line, plane
C. segment, angle, point
D. plane, helicopter, jet
42. _________ Line A passes through (-3, 5) and (1, -3). What is the
slope of the line that is parallel to line A?
A. 2
C. -2
(Language of Geometry)
Parallel lines have the same slope.
Perpendicular lines have opposite
reciprocal slopes.
B.
D. -
Graph the points and count
the formula
or use
43. _________ Line A passes through (2, 5) and (-1, 1). What is the
slope of the line that is perpendicular to line A?
A.
C. -
B.
D. -
(Language of Geometry)
Parallel lines have the same slope.
Perpendicular lines have opposite
reciprocal slopes.
Graph the points and count
or use
the formula
44. A line is perpendicular to the line for the equation:
4. What is the slope of the perpendicular line?
A.
B.
C.
D.
(Language of Geometry)
Parallel lines have the same slope.
Perpendicular lines have opposite
reciprocal slopes.
Graph the points and count
the formula
45. Which could be the coordinates of the fourth vertex of
rectangle if the other coordinates are X (-1,5), Y (6,-2),
and Z (3, -5) ?
A. (-5, 3)
B. (-4, 2)
C. (0, -2)
D. (2, 8)
(Quadrilateral Unit)
Graph
or use
(Quadrilateral Unit)
46. Below are three statements about the figure.
I. ∠ ≅ ∠
II. ∠ ≅ ∠
III.
Which statement can be proven?
A. I only
B. II only
C. I and II
D. II and III
≅
47. What is the area of ∆
in square units?
(Triangles Unit)
Step #1: Draw a rectangle around
the triangle so each vertex of the
triangle is on the rectangle.
Step #2: Find the area of the
rectangle.
Step #3: Find the area of all 3 right
triangles.
Step #4: Subtract the area of the 3
rights triangles from the total area
of the rectangle.
A. 60.5
B. 72
C. 84.5
D. 144
Alternate Interior
Angle Bisector
Angles
1
2
Centroid
3
Circumcenter
4
Complementary
Corresponding
Angles
Angles
5
6
Dilation
7
Incenter
8
Linear Pair of
Median
Angles
9
10
Parallel Lines
Parallelogram
12
11
Perimeter
Perpendicular
Bisector
13
14
Perpendicular Lines
15
Rectangle
16
Rhombus
Rigid
Transformation
18
17
Similar Figures
19
Slope
20
Square
Supplementary
Angles
21
22
Undefined Terms
Vertical Angles
23
24
25
26
27
28
29
30
scale factor = ½
center E
31
32
∠APD ≅ ∠CPB
Construction:
33
≅
in a triangle:
, m∠CMA = 90°, M is midpoint of
34
42 + 62 = x2
52 = x2
7.2 = x
P = 4 + 6 + 7.2 = 17.2
36
35
37
∠MON and ∠PON form a ___
38 Construction:
in a triangle:
40
39
41 42 ∆ABC ~ ∆DEF
(6, 6)
43
45
47
44
46
48
A parallelogram with four right angles.
A point is a location. It has no size.

Diagonals are congruent
A line is a series of points that extend in both

Diagonals are bisected
directions without end.

Both pairs opposite sides parallel

Both pairs opposite sides congruent
49
A plane is a flat surface with no thickness. It
extends without end.
50
These lines intersect to form right angles. Their
This is a similarity transformation. It results in
slopes are opposite reciprocals, for example 2 and
an enlargement or reduction of an image.
-
or
and -
Preserved:

Angle measures (A is congruent to A’, B is
congruent to B’, etc)

Shape (parallel lines remain parallel, shape
remains the same, just different size)

51
52
One figure is a dilation of the other.


53
orientation
Corresponding angles are congruent Sides are proportional Segment connecting the vertex of a triangle
to the midpoint of the opposite side.
54
A parallelogram with four congruent sides and four
right angles.

Diagonals congruent

Diagonals perpendicular

Diagonals bisect opposite angles

Diagonals bisect each other

Opposite sides parallel
55
A parallelogram with four congruent sides

Diagonals bisect each other

Diagonals perpendicular

Diagonals bisect opposite angles

Opposite angles congruent

Opposite sides parallel
56
The distance around a figure. Add up the
Tow angles whose sides form two pairs of
lengths of the sides. You will likely need
opposite rays (formed by the intersection of
Pythagorean Theorem or the Distance formula
2 lines). These angles are congruent.
to calculate the side lengths.
57
58
These transformations are also called isometries. The
Two angles whose sum is 90°. Angles can be
original figure and its image are congruent. They
preserve the following:

Angle measure (angles are congruent)

Distance (side lengths are congruent)

Shape (parallel sides remain parallel, shape does
adjacent or nonadjacent.
not change)
59
60
The center of the circle that is circumscribed
Non adjacent interior angles who lie on
about a triangle. Point of concurrency of the
opposite sides of the transversal. These
perpendicular bisectors. This point is
angles are congruent.
equidistant to the vertices of the triangle.
61
62
The point of concurrency of the medians of a
These angles lie on the same side of the
triangle. This is the center of gravity.
transversal in corresponding positions relative
to the parallel lines. They are congruent.
63
64
Two adjacent, supplementary (sum to
These are coplanar lines that do not intersect.
180°) angles. They form a line.
They have no point in common. These lines have
the same slope and different y-intercepts. For
example:
Y = 3x – 5 and y = 3x – 2
65
Two angles whose sum is 180°. The angles can
be adjacent (linear pair) or nonadjacent.
66
A line that bisects another line or segment into two
congruent pieces and forms a right angle.
In a triangle, this line may or may not begin at the
vertex, but it crosses the opposite side at the
midpoint and forms a right angle. All three of these
67
lines in a triangle are concurrent at the circumcenter.
68
The center of the circle that is inscribed in a
A line that divides an angle into two congruent
triangle. The point of concurrency of the
parts.
angle bisectors of a triangle. This point is
equidistant to the sides of the triangle.
69
In a triangle all three of these lines are
concurrent at the incenter.
70
A quadrilateral with both pairs of opposite
sides parallel.

Diagonals are bisected

Opposite angles congruent

Opposite sides congruent
71
or
Y=
mx + b
The steepness of a line
72
Term
Figure
Definition
Term
Figure
1
13
2
14
3
15
4
16
5
17
6
18
7
19
8
20
9
21
10
22
11
23
12
24
definition
Term
Figure
Definition
Term
Figure
definition
1
29
62
13
35
57
2
39
70
14
33
68
3
45
63
15
41
51
4
43
61
16
44
49
5
36
60
17
46
56
6
30
64
18
27
59
7
31
52
19
42
53
8
34
69
20
47
72
9
39
65
21
40
55
10
26
54
22
28
67
11
38
66
23
25
50
12
48
71
24
32
58
Your exam has 40 questions. If you google the standard, look for the Shmoop.com
entry. It will have additional practice problems (sample assignments)
G.CO.1: Know precise definitions of angle, circle, perpendicular line, parallel line,
and line segment, based on the undefined notions of point, line, distance along a
line, and distance around a circular arc.
1.
3.
2.
4. G.CO.2: Represent transformations in the plane using, e.g., transparencies and
geometry software; describe transformations as functions that take points in the
plane as inputs and give other points as outputs. Compare transformations that
preserve distance and angle to those that do not (e.g., translation versus
horizontal stretch).
5.
7.
6.
8.
G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe
the rotations and reflections that carry it onto itself.
9.
11.
10.
12.
13.
G.CO.4 Develop definitions of rotations, reflections, and translations in terms of
angles, circles, perpendicular lines, parallel lines, and line segments.
14.
15.
16.
G.CO.5:Given a geometric figure and a rotation, reflection, or translation, draw
the transformed figure using, e.g., graph paper, tracing paper, or geometry
software. Specify a sequence of transformations that will carry a given figure onto
another.
17.
G.CO.6: Use geometric descriptions of rigid motions to transform figures and to
predict the effect of a given rigid motion on a given figure; given two figures, use
the definition of congruence in terms of rigid motions to decide if they are
congruent.
18.
19.
20.
21.
22.
A triangle was rotated 90 degrees
counterclockwise and then translated 2
down and 4 left. The final coordinates of
the triangle are: (1, -3), (-2, 0), and (3,
2). What were the original coordinates?
A (1, 1) (4, 4) (6, -1)
B (0, 2) (2, -3) (-3, -1)
C (-1, 3) (2, 0) (-3, -2)
D (3, 7) (8, -2) (6, 4)
G.CO.7 Use the definitions of congruence in terms of rigid motions to show that
two triangles are congruent if and only if corresponding pairs of sides and
corresponding pairs of angles are congruent.
23.
24.
25.
26.
G.CO.8: Explain how the criteria for triangle congruence (ASA, SAS, and SSS)
follow the definition of congruence in terms of rigid motions.
27.
28.
G.CO.9: Prove theorems about lines and angles. Theorems include: vertical
angles are congruent; when a transversal crosses parallel lines, alternate interior
angles are congruent and corresponding angles are congruent; points on a
perpendicular bisector of a line segment are exactly those equidistant from the
segment's endpoints.
29.
31. 30.
32. 33.
G.CO.10: Prove theorems about triangles. Theorems include: measures of
interior angles of a triangle sum to 180°; base angles of isosceles triangles are
congruent; the segment joining midpoints of two sides of a triangle is parallel to
the third side and half the length; the medians of a triangle meet at a point.
34.
35.
36.
G.CO.11: Prove theorems about parallelograms. Theorems include: opposite
sides are congruent, opposite angles are congruent, the diagonals of a
parallelogram bisect each other, and conversely, rectangles are parallelograms
with congruent diagonals.
37.
38.
G.CO.12: Make formal geometric constructions with a variety of tools and
methods (compass and straightedge, string, reflective devices, paper folding,
dynamic geometric software, etc.). Copying a segment; copying an angle;
bisecting a segment; bisecting an angle; constructing perpendicular lines,
including the perpendicular bisector of a line segment; and constructing a line
parallel to a given line through a point not on the line.
39. 40.
41.
G.CO.13: Construct an equilateral triangle, a square, and a regular hexagon
inscribed in a circle.
G.SRT.1: Verify experimentally the properties of dilations given by a center and a
scale factor:
42.
43.
44.
G.SRT.2: Given two figures, use the definition of similarity in terms of similarity
transformations to decide if they are similar; explain using similarity
transformations the meaning of similarity for triangles as the equality of all
corresponding pairs of angles and the proportionality of all corresponding pairs of
sides.
G.SRT.3: Use the properties of similarity transformations to establish the AA
criterion for two triangles to be similar.
45.
46.
47.
G.SRT.4: Prove theorems about triangles. Theorems include: a line parallel to
one side of a triangle divides the other two proportionally, and conversely; the
Pythagorean Theorem proved using triangle similarity.
48.
G.SRT.5: Use congruence and similarity criteria for triangles to solve problems
and to prove relationships in geometric figures.
G.C.3: Construct the inscribed and circumscribed circles of a triangle, and prove
properties of angles for a quadrilateral inscribed in a circle.
49.
50.
51.
A (4, 6)
B (6, 4) C (3, 3) D (1, 2)
G.GPE.5: Prove the slope criteria for parallel and perpendicular lines and use
them to solve geometric problems (e.g., find the equation of a line parallel or
perpendicular to a given line that passes through a given point).
G.GPE.6: Find the point on a directed line segment between two given points
that partitions the segment in a given ratio.
52.
53.
54.
55.
Where should you plot point X so that
PX is of the length of PQ?
A. (4, 0)
B (6, 0)
C (7, 0)
D (8, 0)
Where should you plot X so it divides PQ in a
ratio of 3:4?
A. (5 , 0)
B (4 , 0)
C 4 , 0)
D (3 , 0)
G.GPE.7: Use coordinates to compute perimeters of polygons and areas of
triangles and rectangles, e.g., using the distance formula.
56.
57.
58.
59.
60 .