Download Geometry Midterm Exam Review

Geometry MidTerm Exam Review
Mrs. Gilliland
Name_________________________________Date__________Period______
1. Write an equation of the line perpendicular to the given line that contains P.
P(7, -5);
2. Anna is using a straightedge and compass to do the construction shown below. What construction does she
appear to be doing?
3.
What is the first step in constructing the angle bisector of angle A?
4. Write the notation for the composition of a dilation of scale factor 2 followed by a translation of 3 units to the
right.
5. Given that ∆𝐾𝑂𝑁~∆𝐿𝑂𝑀 find the coordinates of L and the scale factor.
6.
How can you justify that 𝑌𝐾 ≅ 𝑅𝐵, given ∆𝐵𝑅𝑀 ≅ ∆𝐾𝑌𝑍 ?
7. Which additional piece of information would allow you to prove that the triangles are congruent by the HL
theorem?
8. Given:
and
ASA congruence postulate?
. What other piece of information is needed to show
by
9.
In the given triangle
. Find the measure of
.
10. What point of concurrency is created by the lines shown in the following construction?
11.
12.
13.
Multiple Response
Identify one or more choices that best complete the statement or answer the question.
____ 14. A circle is inscribed in a triangle. Check all the properties that apply to this construction.

The center of the circle is
constructed using angle bisectors

The center of the circle is called
the incenter

The center of the circle is
constructed using the altitudes of
the triangle
The center of the circle is
equidistant from the vertices of
the triangle

The center of the circle is called
the circumcenter

The center of the circle is
constructed using perpendicular
bisectors of the sides

____ 15. Which of the following choices could represent a line segment? Check all that apply.

A drinking straw

A laser beam

The leg of a table

A city on a map
Short Answer
16. Find the angle measures of m and n.
17. What must be true about the slopes of two perpendicular lines, neither of which is vertical?
 The slopes have product –1.

One of the slopes must be 0.

The slopes are equal.

The slopes have product 1.
18. ∆LMP has coordinates L(3,4), M(6,6), and P(5,5). A translation maps point L to L’ at (7, 24). What are the coordinates for M’ and for P’ for this translation?
19. Use the diagram to answer parts a and b below. The scale in the diagram is 1:
a. The triangle is transformed according to the mapping
of D’, E’, F’
D’ __________ E’ ____________
F’ ___________
. Write the coordinates
b. The transformed triangle from part a is reflected across the y-axis. What are the coordinates
of D”, E”, F”?
D” __________ E” ____________
F” ___________
Essay
20. Transversal t intersects parallel lines a and b.
a.
Identify a pair of alternate interior angles.
b.
Prove that these alternate interior angles are congruent. (Use picture from 20a)
Statement
1. a || b
2.
3. _________________________
4.
Reasoning
1. Given
2. _______________________
3. Corresponding Angles Theorem
4. Transitive Property of Congruence
21. Graph Quadrilateral ABCD where the vertices are A(-3, 0), B(0, 2), C(4, 1), and D(-5, -5).
a. Find the slope of each side.
b. Are the opposite sides of ABCD parallel? Explain how you know if they are or are not.
c. Are the adjacent sides of ABCD perpendicular? Explain how you know if they are or are not.
22. What kind of line is being constructed in this series of diagrams?
23. If
𝑃
𝑄
=
𝑅
𝑆
a.
, which of the following is NOT true?
𝑅
𝑆
=
𝑃
𝑄
𝑏. 𝑃𝑅 = 𝑆𝑄
c.
𝑄
𝑃
=
𝑆
𝑅
d. 𝑃𝑆 = 𝑅𝑄
24. Mr. Jones has taken a survey of college students and found that 1 out of 5 students are liberal arts majors. If a college
has 12,000 students, what is the best estimate of the number of students who are liberal arts majors?
25. If ΔABC ~ ΔPBQ, then which of the following proportions is NOT true?
a.
26.
b.
c.
Which triangles are congruent by ASA?
F
T
A
(
V
))
((
(
)
G
H
C
U
27. Find the value of x.
16
3x – 4
B
d.
Use the diagram to find the following.
h
a
1
8
b
28a. Identify a pair of alternate exterior angles.
28b. What are three pairs of corresponding angles?
2
3
7
29.Find the value of x for which l is
parallel to m. The diagram is not to scale.
4
6
5
80°
( 3 x - 43 )º
30. Find the value of k. The diagram is
not to scale.
62°
45°
k°
l
m