Right Triangle Similarity

Question 1

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

Revolt · Accepted Answer

Answer image: https://media.edgenuity.com/EVresources/801366df56e8b0bf2469d89b7c34e8e9.png

Question 2

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.

Revolt · Accepted Answer

cf

Question 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.

Revolt · Accepted Answer

c/b

Question 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.

Revolt · Accepted Answer

cf + ec

Question 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.

Revolt · Accepted Answer

c

Question 6

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

Revolt · Accepted Answer

Answer image: https://media.edgenuity.com/EVresources/71e5fd2ca63cc8840666eee88752226c.png

Question 7

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

Revolt · Accepted Answer

Answer image: https://media.edgenuity.com/EVresources/fdd470cade98de3af5e21be3f2557579.png

Question 8

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.

Revolt · Accepted Answer

a/f

Question 9

Which similarity statement is true?

Revolt · Accepted Answer

ΔSRQ ~ ΔRTQ

Right Triangle Similarity Answers

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