Question

26. Two angle measures of different triangles

are listed below.

Triangle A: m_1= 36º, mz2 = 88°

Triangle B: m_1 = 88°, m_2 = 54°

=

Are the two triangles similar? How do you

know?

Answer 1

Explanation:

To determine if two triangles are similar, we need to check if their corresponding angles are congruent and their corresponding sides are proportional.

Let's check the corresponding angles of the two triangles:

Triangle A has angles of 36°, 88°, and (180° - 36° - 88°) = 56°.

Triangle B has angles of 88°, 54°, and (180° - 88° - 54°) = 38°.

We can see that the two triangles have one pair of congruent angles (88° in both triangles). However, they do not have any other pairs of congruent angles. Therefore, the triangles are not similar based on angle congruence.

We can also check if the corresponding sides of the triangles are proportional using the side-angle-side (SAS) similarity criterion. However, since we have already determined that the triangles are not similar based on angle congruence, we do not need to check for side proportions.

Therefore, we can conclude that the two triangles are not similar.