MATH SOLVE

4 months ago

Q:
# Which triangle is △ABC similar to and why? △ABC is similar to △DEF by AA Similarity Postulate . △ABC is similar to △GHI by AA Similarity Postulate . △ABC is similar to △JKL by AA Similarity Postulate . △ABC is not similar to any of the triangles given. NOTE: Figures are not drawn to scale. Four triangles are given. Triangle A B C, triangle D E F, triangle G H I, and triangle J K L. Angle A is 20 degrees. Angle B is 80 degrees. Angle D is 18 degrees. Angle E is 80 degrees. Angle G is 20 degrees. Angle H is 70 degrees. Angle K is 80 degrees. Angle L is 80 degrees.

Accepted Solution

A:

The answer would be, it is △JKL by the AA Similarity Postulate.

Explanation for this would be:

For ΔABC

m∠A + m∠B + m∠C = 180°

20° + 80° + m∠C = 180°

100° + m∠C = 180°

m∠C = 80°

Therefore, the two angle pairs are congruent ⇒ △ABC ~ △JKL

Explanation for this would be:

For ΔABC

m∠A + m∠B + m∠C = 180°

20° + 80° + m∠C = 180°

100° + m∠C = 180°

m∠C = 80°

Therefore, the two angle pairs are congruent ⇒ △ABC ~ △JKL