AnswersCR CCSS Math 2 S2 M2960OXUsing Triangle Similarity Theorems

Using Triangle Similarity Theorems Answers

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1
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Which similarity statement is true?

A
ΔSRQ ~ ΔTRS
B
ΔSRQ ~ ΔRTQ
C
ΔSRQ ~ ΔRTS
D
ΔSRQ ~ ΔQRT
2
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You can use the similar triangles formed by the altitude to write ratios for corresponding sides. Using ratios from the large and medium triangles, = . This can be rewritten as = a2. Using ratios from the large and small triangles, = . This can be rewritten as b2 = ec. By substitution, a2 + b2 =. You can then factor as a2 + b2 = c(f + e). From the large triangle, you know (f + e) =. So, a2 + b2 = c2 by using substitution.

A
af
B
cf
C
ch
3

You can use the similar triangles formed by the altitude to write ratios for corresponding sides. Using ratios from the large and medium triangles, = . This can be rewritten as = a2. Using ratios from the large and small triangles, = . This can be rewritten as b2 = ec. By substitution, a2 + b2 =. You can then factor as a2 + b2 = c(f + e). From the large triangle, you know (f + e) =. So, a2 + b2 = c2 by using substitution.

A
b/a
B
c/b
C
b/c
D
b/f
4

You can use the similar triangles formed by the altitude to write ratios for corresponding sides. Using ratios from the large and medium triangles, = . This can be rewritten as = a2. Using ratios from the large and small triangles, = . This can be rewritten as b2 = ec. By substitution, a2 + b2 =. You can then factor as a2 + b2 = c(f + e). From the large triangle, you know (f + e) =. So, a2 + b2 = c2 by using substitution.

A
cf + ec
B
cf + ac
C
ch + ah
D
ch + cf
5

You can use the similar triangles formed by the altitude to write ratios for corresponding sides. Using ratios from the large and medium triangles, = . This can be rewritten as = a2. Using ratios from the large and small triangles, = . This can be rewritten as b2 = ec. By substitution, a2 + b2 =. You can then factor as a2 + b2 = c(f + e). From the large triangle, you know (f + e) =. So, a2 + b2 = c2 by using substitution.

A
a
B
b
C
c
D
h
6

Which proportion satisfies the geometric mean (altitude) theorem for the triangle?

A
Option
B
Option
C
Option
D
Option
7

Use the geometric mean (altitude) theorem. What is the value of m?

A
4
B
Option
C
Option
D
160
8

Use the geometric mean (leg) theorem. What is the value of a?

A
Option
B
Option
C
Option
D
Option
9

You can use the similar triangles formed by the altitude to write ratios for corresponding sides. Using ratios from the large and medium triangles, = . This can be rewritten as = a2. Using ratios from the large and small triangles, = . This can be rewritten as b2 = ec. By substitution, a2 + b2 =. You can then factor as a2 + b2 = c(f + e). From the large triangle, you know (f + e) =. So, a2 + b2 = c2 by using substitution.

A
f/a
B
a/f
C
f/h
D
h/f

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