Name:_____________________________________ Class Period:_________ Score:________/50 Assignment # ____
35
Geometry Study Guide You MUST justify and simplify your solution(s) to receive credit.
1. For the triangles below, the perimeter of ∆ABC equals the
perimeter of ∆DEF. If ∆ABC is equilateral, what is the length of
̅̅̅̅
𝐴𝐵 ?
2. In the right triangle below,
mC is less than mA, list
the sides in order from the
shortest to the longest
B
A
E
14
13
A
D
C
F
15
B
C
3. Triangle DEF is similar to triangle XYZ, as shown 4. Eileen drew two similar triangles for an art
below. What is the measure of angle Y ?
project, as shown below. Find the missing side.
E
14 cm
D
12 cm
33o
x
Y
84o
63o F
7 cm
6 cm
6
9
Z
X
12
5. In the figure below, if s ∥ t, what does c equal in 6. What is the measure of the exterior angle in the
triangle below ?
terms of a and b ?
bo
co
63o
s
t
ao
27o
7. Given that ̅̅̅
𝐽𝐾 ≅ ̅̅̅̅
𝑅𝑆, J ≅ R, and K ≅ S. 8. In the triangles below, what is the average
(arithmetic mean) of w, x, y, and z ?
What theorem proves ∆JKL ≅ ∆RST ?
K
R
60o
xo
J
wo
L
S
10. ̅̅̅̅̅
𝑌𝑊 is an altitude of right ∆XYZ, as shown in
the diagram below. Complete the similarity
statement ∆XYZ ∼ ___________ ∼ ___________
I
(5x + 9)o
(5x – 3)o
zo
T
9. Find the measure of H.
H
yo
(7x + 4)o
J
You must justify and simplify your solution(s) to receive credit. Failure to show your work or insufficient explanation will result no credit.
̅̅̅̅ is also the
11. In the diagram below, altitude 𝐷𝐺
̅̅̅̅
median to 𝐸𝐹 of ∆DEF. Classify ∆DEF
D
G
E
12. Classify ∆ABC if it has the following
properties:
 mA + mC = 110o
 mA = mC
F
13. At a certain time of day, a 1.8m tall person
standing next to the Washington Monument
casts a 0.7m shadow. At the same time, the
Washington Monument casts a 65.8m shadow.
How tall is the Washington Monument?
14. In the figure below, ∆PQR and ∆STR are right
triangles. The length of segment SR is 9. What
is the length of segment TQ?
– R
9
15
21
S
– P
15. Two points M and N are shown on the graph
below. What is the distance between the two
points? Write your answer in the simplest
radical form.
T
Q
16. Write the equation of the line that is
perpendicular to line l in the graph.
M
(4, 6)
l
N
(–5, –3)
17. Write the equation of the line that is parallel to
line l in the graph.
l
18. On the coordinate grid below, the line EF
contains point E(2,0) and F(5,6). What is the
slope of line EF ?
You must justify and simplify your solution(s) to receive credit. Failure to show your work or insufficient explanation will result no credit.
19. Triangle ABC is similar to triangle EDC shown
below. Write the equation that could be used to
determine x, length of CD. What is ̅̅̅̅̅
𝐶𝐷 ?
20. Write the inverse of the following statements
and determine the true of value of its inverse.
If a triangle is equilateral, then it is isosceles.
C
x
7
D
E
6
A
B
–
–
8
21. Given XY, XZ, and YZ are the lengths of midsegments. Find the perimeter of triangle NHP.
P
5
X
Y
4
22. In the figure below, triangle UVT is similar to
triangle VNM. What is the value of segment
MV ?
x
3
N
H
Z
23. In the diagram below, line EF is parallel to line 24. Line a is represented by the equation
1
JK. What is the value of x ?
𝑦 = 3 𝑥 + 7. Line b is perpendicular to line
a and passes through point (– 5, 5). Write the
F
E
⦁
⦁o
equation of line b in slope-intercept form.
o
35
x
o
112⦁o
J
⦁145
K
̅̅̅̅ , and R 26. Write the converse of the given conditional
25. In the diagram below, ̅̅̅̅
𝑅𝑈 bisects 𝑆𝑉
statement and find the true value each
is congruent to U. Identify the postulate or
statement. If x and y are negative integers,
theorem that proves ∆RST ≅ ∆UVT
then their quotient is always positive.
S
U
T
R
V
You must justify and simplify your solution(s) to receive credit. Failure to show your work or insufficient explanation will result no credit.
27. A ramp, forming an angle of 18o with the ground, extends at a horizontal distance of 78 feet toward a
building. Support pillars are to be placed 22 feet and 44 feet from the building, as shown in the
diagram below.
18o
|
|
|
78 ft
44 ft
22 ft
|
|
|
(A) If the building is 25.3 ft high, find the following measurements, rounded to the nearest tenth of a
meter.
i. The height of the pillar that is 22 ft from the building.
ii. The height of the pillar that is 44 ft from the building.
(B) Explain why the triangles formed by the support pillars and the building are all similar.
28. ST is the midsegment of triangle ABC. Find the
values of the variables x, y, and z in the
diagram.
A
38
B
x
29. The base angles of isosceles ∆CAT have
measures of (5x – 5)o and (3x + 7)o. The
vertex of isosceles ∆DOG has a measure of
(7y + 2)o.
a. What is the measures of the base angles of
∆CAT ?
z
S
b. What is the measure of the vertex in ∆CAT ?
125o
T
y
12
C
c. What value of y would make the triangles
similar? Explain why.