Name___________________________________________ Date___________________ Class_______________
7.3 Similar Triangles Practice
Write a similarity statement for the three similar triangles in the diagram. Then
complete the proportion.
1.
?
GF
DG
EG
2.
MN
?
MQ
PQ
3.
?
RU
RT
RS
Complete and solve the proportion. Answers should be exact (simplified fractions
or radicals).
4.
x
12
?
8
5. 15
x
x
?
Find the exact value(s) of the variable(s).
7.
8.
10.
11.
6. 9
x
9.
12.
x
?
Tell whether the triangle is a right triangle. If so, find the length of the altitude to
the hypotenuse. Round decimal answers to the nearest tenth.
13.
14.
15.
Find the exact lengths of AC and BD.
16.
17.
18.
Find the geometric mean of each pair of numbers. Write answers in simplest
radical form.
19. 16 and 25
20. 3 and 15
21. 18 and 30
22. Complete the proof:
GIVEN: ΔXYZ is a right triangle with m ∠XYZ = 90º.
VW || XY ,
YU
is an altitude of ΔXYZ.
PROVE: ΔYUZ ~ ΔVWZ
Statements
1. XYZ is a right
Reasons
with altitude YU
.
1. _________________________________
2. XYZ ~ YUZ
2. _________________________________
3. VW || XY
3. _________________________________
4. ∠ VWZ
5. ∠ Z
∠ XYZ
∠ Z
4. _________________________________
5. _________________________________
6. _________________________________
6.AA Similarity Postulate
7. YUZ ~ VWZ
7. _________________________________
Answer Key -- Lesson 7.3
1. ∆FED ~ ∆FGE ~ ∆EGD; EG
2. ∆MQP ~ ∆MNQ ~ ∆QNP; NQ
3. ∆RST ~ ∆RUS ~ ∆SUT; RS
4. 12; 18
5. 5; 5 3
6. 20;
6 5
7. a = 3
8. x = 4 3
9.
b
25
6
10. w = 3
11. x = 49/4, y = 15/4, z =
12.
a
42 2 , b
3
40 , c
7 15
4
53 1
3
yes; 9.1
no
yes; 15.4
AC 50, BD 24
AC 2, BD 15
18. AC 7, BD 10
13.
14.
15.
16.
17.
19. 20
20. 3√5
21. 6√15
22. 1.Given
2. Similar Right Triangles Theorem
3.Given
4.Corresponding Angles Postulate
5. Reflexive Property of Congruence
6. ΔXYZ ΔVWZ
7.Transitive Property (both similar to ΔXYZ so both similar to each other)