Download Geometry Chapter 8 Review The given polygons are similar. Find

Geometry Chapter 8 Review
The given polygons are similar. Find the value of x.
1.
2.
3.
Find the scale factor. Then list all the pairs of congruent angles and write the ratios of the corresponding
side lengths in a statement of proportionality.
4.
5.
In Exercises 6 and 7, find the scale factor. Then list all pairs of congruent angles and
write the ratios of the corresponding side lengths in a statement of proportionality.
6. ∆𝐿𝑀𝑁 to ∆𝑄𝑅𝑆
7. ABCD to EFGH
Show that the triangles are similar. Write a similarity statement.
8.
9.
Can the given information be used to prove ∆𝑨𝑩𝑪~∆𝑬𝑫𝑪? Explain your reasoning.
10. ED  8, DC  10, EC  12, AB  12,
BC  15, AC  21
11. ED  7, DC  9, AB  10.5, BC  13.5,
mBAC  mBCA  105
The triangles in each pair are similar. Find the value of x.
12. ∆𝐷𝐵𝐶~∆𝑇𝑅𝑆
13. ∆𝐴𝐵𝐶~∆𝐷𝐸𝐶
14. ∆𝐴𝐵𝐸~∆𝐴𝐶𝐷
15. Your geometry class goes on a field trip to the zoo. If an 18-foot tall tree casts a 9 foot-long shadow,
how tall is an adult giraffe that casts a 7-foot shadow?
16. A 4-foot tall girl stands 6.5 feet from a lamp post at night. Her shadow from the light is 2.5 feet long.
How tall is the lamp post?
Use the figure to complete the proportion.
17.
EF
BA

FG
?
18.
CB
?

BA
EF
19.
DC
?

FA
AG
20.
GF
GD

FA
?
Find the value of x.
21.
22.
23.
24. Your friend is hitting a golf ball toward the hole. The line from your friend to
the hole bisects the angle formed by the lines from your friend to the oak
tree and from your friend to the sand trap. The oak tree is 250 yards from
him. The sand trap is 375 yards from him. The hole is 225 yards from the
sand trap. How far is the hole from the oak tree?
25. Use the diagram to answer the following:
a. Find the scale factor of ∆𝐴𝐵𝐶 𝑡𝑜 ∆𝑋𝑌𝑍.
b. Find mX .
c. Find CD.
d. Find the area of ∆𝐴𝐵𝐶. Then find the area of ∆𝑋𝑌𝑍.
e. Find the ratio of the area of ∆𝐴𝐵𝐶 to the area of ∆𝑋𝑌𝑍.
f. Find BC and YZ . Explain your reasoning.
g. Find the ratio of the perimeter of ∆𝐴𝐵𝐶 to the perimeter of ∆𝑋𝑌𝑍.
In Exercises 26 and 27, the figures are similar. Find the missing value.
26. If 𝐴𝐵𝐶𝐷𝐸~𝐹𝐺𝐻𝐼𝐽, AC = 6 cm, FH = 10 cm, and the area of ABCDE = 320 cm2, then the
area of FGHIJ = ______________.
27. The ratio of the corresponding midsegments of two similar triangles is 4:5. What is the
ratio of their areas?
Answers:
1. 20
6
5
2. 10
3. 8
4. ; C  D, A  F , B  E;
AC
BC
AB


DF
DE
EF
2
5
5. ; A  E, B  F , C  G, D  H ;
6. 3;  L  Q,  M   R,  N   S ,
2
5
AB
BC
AD
DC



EF
FG
EH
GH
LM
MN
NL


QR
RS
SQ
7. ;  A   E,  B   F , C  G,  D   H ,
AB
BC
CD
DA



EF
FG
GH
HE
8. Sample answer: It is given that BAC  EDC, and BCA  ECD by the Vertical Angles Congruence
Theorem (Thm. 2.6). So, ∆𝐵𝐴𝐶~∆𝐸𝐷𝐶 by the AA Similarity Theorem (Thm. 8.3); ∆𝐵𝐴𝐶~∆𝐸𝐷𝐶
9.Sample answer: Because
BC
EC

and BCA  ECD by the Vertical Angles Congruence Theorem
AC
DC
(Thm. 2.6), ∆𝐵𝐴𝐶~∆𝐸𝐷𝐶 by the SAS Similarity Theorem (Thm. 8.5); ∆𝐵𝐴𝐶~∆𝐸𝐷𝐶
10. no; Based on this information, the triangles are not similar because the sides are not all proportional.
11. no; Although the proportion
ED
AB

DC
BC
is true, there is not enough information given to determine
whether ABC  CDE.
12. 9
13. 15
14. 6
15. 14 ft
16. 14.4 ft
17. AG
18. ED
19. CG
20. CD
21. 6
22. 11.2
23. 4.5
b. 67°
c. 12
d. 60; 540
e. 9
24. 150 yd
25. a. 3
g. 3
f. 13, 39; By the SAS Congruence Theorem (Thm. 5.5), ! ADC  ! BDC and ! XWZ  ! YWZ . Because
corresponding parts of congruent triangles are congruent, BC  13 and YZ  39.
26. 16:25
8
27. 888 9 cm2