Download Midterm Review Packet Name: What is the slope of a line

Midterm Review Packet
Name: _______________
1. What is the slope of a line perpendicular to the line whose equation is
1)
?
2)
3)
4)
2. What is the equation of a line passing through
equation
?
1)
and parallel to the line represented by the
2)
3)
4)
3. A line segment has endpoints
?
1)
2)
and
. What are the coordinates of the midpoint of
3)
4)
4. Point M is the midpoint of
. If the coordinates of A are
, what are the coordinates of B?
1)
2)
3)
4)
and the coordinates of M are
5. Find, in simplest radical form, the length of the line segment with endpoints whose coordinates are
and
.
6. Which illustration shows the correct construction of an angle bisector?
1)
3)
2)
4)
7. Which diagram shows the construction of the perpendicular bisector of
1)
2)
3)
4)
?
8. Which geometric principle is used to justify the construction below?
1) A line perpendicular to one of two parallel
lines is perpendicular to the other.
2) Two lines are perpendicular if they intersect
to form congruent adjacent angles.
3) When two lines are intersected by a
transversal and alternate interior angles are
congruent, the lines are parallel.
4) When two lines are intersected by a
transversal and the corresponding angles are
congruent, the lines are parallel.
9. Which diagram shows the construction of an equilateral triangle?
10. In
1)
2)
3)
4)
,
right
scalene
isosceles
equilateral
,
, and
. Which type of triangle is
?
11. Tina wants to sew a piece of fabric into a scarf in the shape of an isosceles triangle, as shown in the
accompanying diagram.
What are the values of x and y?
1)
2)
12. In the diagram below of
.
What is
1) 5
2) 20
3) 25
4) 55
?
, side
3)
is extended to point D,
4)
,
, and
13. Phil is cutting a triangular piece of tile. If the triangle is scalene, which set of numbers could
represent the lengths of the sides?
1)
2)
3)
4)
14. On the banks of a river, surveyors marked locations A, B, and C. The measure of
the measure of
.
and
Which expression shows the relationship between the lengths of the sides of this triangle?
1)
2)
3)
4)
15. The diagram below shows the construction of the center of the circle circumscribed about
This construction represents how to find the intersection of
1) the angle bisectors of
2) the medians to the sides of
3) the altitudes to the sides of
4) the perpendicular bisectors of the sides of
.
16. In
shown below, P is the centroid and
What is the length of
1) 6
2) 9
3) 3
4) 12
.
?
17. The measures of five of the interior angles of a hexagon are 150°, 100°, 80°, 165°, and 150°. What
is the measure of the sixth interior angle?
1) 75°
2) 80°
3) 105°
4) 180°
18. One piece of the birdhouse that Natalie is building is shaped like a regular pentagon, as shown in
the accompanying diagram.
If side AE is extended to point F, what is the measure of exterior angle DEF?
1) 36°
2) 72°
3) 108°
4) 144°
19. The measure of an interior angle of a regular polygon is 120°. How many sides does the polygon
have?
1) 5
2) 6
3) 3
4) 4
20. If point
1)
2)
3)
4)
is rotated counterclockwise 90° about the origin, its image will be point
21. What is the image of point
1)
2)
3)
4)
22. The image of point
1)
2)
3)
4)
after a reflection in the x-axis?
when reflected in the y-axis is
23. What are the coordinates of point P, the image of point
1)
2)
3)
4)
24. What is the image of point
1)
2)
3)
4)
under a R180°?
after a reflection in the line
?
25. A translation moves
the same translation?
1)
2)
3)
4)
26. What is the image of point
by a R90°?
1)
2)
3)
4)
to
. What are the coordinates of the image of point
under
after the composition of transformations defined by ry=x followed
27.A transformation of a polygon that always preserves both length and orientation is
1) dilation
2) translation
3) line reflection
4) glide reflection
27. When a dilation is performed on a hexagon, which property of the hexagon will not be preserved in
its image?
1) parallelism
2) orientation
3) length of sides
4) measure of angles
28. What is the image of
1)
2)
3)
4)
after a translation of 3 units right and 7 units down?
29. As shown in the diagram below,
is a median of
.
Which statement is always true?
1)
2)
3)
4)
30. Given:
,
is the perpendicular bisector of
Which statement can not always be proven?
1)
2)
3)
4)
31. In the diagram below of
To prove that
and
information is needed?
1)
2)
3)
4)
and
,
, and
are congruent by SAS, what other
.
32. In the diagram of quadrilateral ABCD,
,
Which method can be used to prove
1) AAS
2) SSA
3) SAS
4) HL
33. In the diagram below,
is congruent to
.
Which statement must be true?
1)
2)
3)
4)
34. In the diagram below of
,
.
Using this information, it could be proven that
1)
3)
2)
4)
, and diagonal
?
is drawn.
35. Given:
bisects
at E.
Prove:
36. Given:
Prove:
,
bisects
37. Given:
Prove:
and
,
, C is the midpoint of
and
38. Construct the median of ∆ABC to AC .
B
A
C
39. Construct the altitude of ∆ABC to AC .
B
A
C
40. In the diagram below of
,
,
, and
.
Point P must be the
1) centroid
2) circumcenter
3) incenter
4) orthocenter
41. Which geometric principle is used in the construction shown below?
1) The intersection of the angle bisectors of a
triangle is the center of the inscribed circle.
2) The intersection of the angle bisectors of a
triangle is the center of the circumscribed
circle.
3) The intersection of the perpendicular
bisectors of the sides of a triangle is the
center of the inscribed circle.
4) The intersection of the perpendicular
bisectors of the sides of a triangle is the
center of the circumscribed circle.
42. Triangle ABC has vertices
,
, and
. Determine the point of intersection of the
medians, and state its coordinates. [The use of the set of axes below is optional.]
43. What is the image of the point
1)
2)
3)
4)
under the translation along the vector 3,4 ?
44. Find the coordinates of the point P that lies along the directed line segment from A(1, 2) to B(10, 8)
and partitions the segment in the ratio 2 to 1.
45. Find the coordinates of the point P that lies along the directed line segment from C(-3, -1) to D(7, 6)
and partitions the segment in the ratio 3 to 2.
46. The diagram at right shows the intersection of three lines concurrent at the ______________ of a
triangle.
1)incenter
2) circumcenter
3) centroid
4) orthocenter
47. For a triangle, which two points of concurrence could be located outside the triangle?
1)
2)
3)
4)
incenter and centroid
centroid and orthocenter
incenter and circumcenter
circumcenter and orthocenter
48. Which point is equidistant from the three sides of the triangle?
1) circumcenter
(2) incenter
(3) centroid
(4) orthocenter
49. When AB ll CD and cut by transversal EF , BGH  x  30 and DHG  x 2  4 x . Find X.
F
G
A
H
C
E
50.
B
D
51. Which transformation is not a rigid motion?
1) Line reflection
2) Dilation
3) Rotation
4) Translation
52. The coordinates of
are
,
of its image after the transformation?
1)
2)
3)
4)
53.
54.
, and
. What are the coordinates of the vertices
55. What are the coordinates of the point
1)
2)
3)
4)
56. If the image of A after a dilation of
1)
2)
3)
4)
under the dilation
is
57. In which quadrant would the image of point
1) I
2) II
3) III
4) IV
?
, what are the coordinates of A?
fall after a dilation using a factor of
Transformations with Pictures
58. In the diagram below, under which transformation is
1)
2)
3)
4)
the image of
?
?
59. In the diagram below, under which transformation is
1)
2)
3)
4)
?
dilation
reflection
rotation
translation
60. In the diagram below, which transformation was used to map
1)
2)
3)
4)
the image of
dilation
rotation
reflection
glide reflection
to
?
61. The line 4𝑦 + 3𝑥 = 15 is transformed by a dilation centered at the origin by a factor of 3. What is
the equation its image?
62. Given ∆𝐴𝐵𝐶 ≅ ∆𝑋𝑌𝑍, describe a precise sequence of rigid motions that would map ∆𝐴𝐵𝐶 onto
∆𝑋𝑌𝑍.