Download Name Geometry Semester 1 Review Guide 1 2014

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°
360
𝑛
D. 60°
How many lines of reflection are there?___
where n is number of sides
Number of lines of reflection = n
3. _________ Trapezoid 𝑆𝑊𝐼𝑀 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 ∆𝑀𝑄𝐻 when it is
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)
(transformation unit)
Re-plot on a bigger graph!
5. __________
(transformation unit) *Assume the
rotation is counterclockwise unless
otherwise stated.
̅̅̅̅
A. 𝐻𝐺
Angle of rotation =
360
𝑛
where n is
number of sides.
B. ̅̅̅̅
𝑈𝑃
How many turns is in a 270° rotation?
̅̅
C. ̅̅
𝑇𝑆
Where will EI end up if you turn the
̅̅̅̅
D. 𝐺𝐻
figure that many counterclockwise?
6. ________
(transformation unit)Angle of rotation =
360
𝑛
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
result 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. Bo, they will always result in perpendicular lines
(transformation unit) A rotation is an
example of a rigid transformation!
9. _________ Square ABCD, shown at the right, is translated
up 3 units and right 2 units to
(transformation unit) A translation is an
example of a rigid transformation!!
produce rectangle A’B’C’D’.
Which statement is true?
A
̅̅̅̅
𝐴𝐵 ∥ ̅̅̅̅̅̅
𝐴′𝐵′ and ̅̅̅̅
𝐵𝐶 ∥ ̅̅̅̅̅̅
𝐵′𝐶′
B
̅̅̅̅̅̅ and 𝐵𝐶
̅̅̅̅̅̅
̅̅̅̅ ⊥ 𝐴′𝐵′
̅̅̅̅ ⊥ 𝐵′𝐶′
𝐴𝐵
C
2𝐴𝐵 = 𝐴′𝐵′ and 3𝐵𝐶 = 𝐵′𝐶′
D
𝐴𝐵 + 2 = 𝐴′𝐵′ and 𝐵𝐶 + 3 = 𝐵′𝐶′
(transformation unit) The line y = 2 is a
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?
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)
Angle bisector: line that divides an
A. The medians of a triangle are concurrent
angle into two congruent parts
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
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:
y=- x–4
What is the slope of line Q?
B. -
C. 2
3
(Language of Geometry)
Perpendicular lines have opposite
2
3
2
𝑥+𝑥 𝑦+𝑦
,
)
2
2
Parallel lines have the same slope.
3
A.
(Language of Geometry)
D.
3
2
2
3
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
A
(4,6)
B
(8,-1)
C
(5,2)
D
(9,1)
P
parallel. Use slope to help find the last
point.
R
Q
21. ___________ What is the coordinate of the midpoint of ̅̅̅̅
𝐴𝐵 ?
(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
(Triangles) Isosceles triangles:
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
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
C. 52
side lengths.
D. 134
24. __________ 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 ̅̅̅̅̅
𝐹′𝐺′ ?
A. 2 units
B. 3 units
C. 5 units
D. 6 units
(Transformatons)
The center is the fixed point. The
other vertices will be twice as far from
(2, 2)
25. __________ Which of the following is necessary to prove
(𝑇𝑟𝑖𝑎𝑛𝑔𝑙𝑒𝑠) ∠3 is exterior angle. ∠1 and
that a triangles’s exterior angle equals the sum of the two
∠2 are
remote interior angles?
remote
A. the definition of complementary angles
interior
angles
B. The definition of angle bisector
C. The definition of supplementary angles
D. The definition of congruent triangles
26. _________ A segment connects the midpoints on two
sides of a triangle. What is true about this segment (the
midsegment)?
(Triangles ) ̅̅̅̅̅
𝐷𝐸 is a midsegment
1
̅̅̅̅
𝐷𝐸 = ̅̅̅̅
𝐵𝐶
2
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 𝑆 are the midpoints
of 𝑋𝑊 and 𝑊𝑌, respectively.
(Triangles)
̅̅̅̅ is the midsegment! See #26
𝑅𝑆
What does the midpoint theorem tell us
̅̅̅̅ and 𝑋𝑌
̅̅̅̅?
about the relationship between 𝑅𝑆
̅̅̅̅ is ½ the length of 𝑋𝑌
̅̅̅̅
A. 𝑅𝑆
̅̅̅̅ is twice the length of 𝑋𝑌
̅̅̅̅
B. 𝑅𝑆
̅̅̅̅ and 𝑋𝑌
̅̅̅̅ are not related by that theorem
C. 𝑅𝑆
̅̅̅̅ and 𝑋𝑌
̅̅̅̅ are equal in length
D. 𝑅𝑆
29. __________ Which diagram shows a triangle
drawn so that it is congruent to
A.
B.
C.
D.
?
(Triangles) Congruent means equal in
size/measure. Use patty paper if
necessary.
30. __________ In the diagram below, what is the measure
of ∠𝐸 if the triangles ∆𝐴𝐵𝐶and ∆𝐷𝐸𝐹 are
similar?
(Triangles)
**In similar triangles, corresponding
angles are congruent!
A. 30°
B. 60°
C. 90°
D. 70°
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
?
A. SAS beause both are
right triangles, JK is
congruent to J’K’ and KL is
congruent to K’L’
B. ASA because both are
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’
(Triangles)
You must have 3 pairs of congruent
angles and sides to use ASA or SAS.
The sides and angles must be
corresponding!!
Try highlighting the information in the
multiple choices to see if the sides and
angles correspond.
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
is taken to
,
is taken to
, and
is taken to
is taken to
,
is taken to
, and
is taken to
C.
.
D.
.
(Triangles)
.
is taken to
.
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
(Triangles)
34. _________ Which statement correctly completes
the sentence below?
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
cont on next page
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

B. Jenny should have constructed
an inscribed circle. Circle O is
circumscribed.
Circumcircle/circumscribed
circle: around the polygon

altitudes of the triangle to find
the incenter.
Incircle/inscribed circle: inside
Medians are concurrent at
centroid

Angle bisectors are concurrent
at incenter

Perpendicular bisectors are
concurrent at circumcenter
C. Jenny should have used the bisectors of angles X, Y, and Z to find
the incenter.

Altitudes are concurrent at
orthocenter
D. Jenny should have put points A, B, and C at the midpoints of the
triangle.
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)
A. left 8 down 12
(Transformations)
〈𝑥, 𝑦〉
X is the horizontal slide
B. right 8 down 12
Y is the vertical slide
41. _________ The translation vector 〈−8, 12〉 means to go:
C. left 8 up 12
D. right 8 up 12
42. _________ What is the line of reflection?
A. x = -2
(Transformations)
Hoy Vux
Horizontal lines are of the form
B. x –axis
y=k
C. y = -2
x=h
D. y- axis
Vertical lines are of the form
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.
1
2
D. -
1
2
formula
𝑟𝑖𝑠𝑒
𝑟𝑢𝑛
or use the
𝑦2 −𝑦1
𝑥2 −𝑥1
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.
4
3
C. -
B.
3
4
D. -
Perpendicular lines have opposite reciprocal
4
3
slopes.
3
4
Graph the points and count
formula
𝑦2 −𝑦1
𝑥2 −𝑥1
𝑟𝑖𝑠𝑒
𝑟𝑢𝑛
or use the