Right Triangle Similarity Answers

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

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.

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.

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.

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.