Question

1. decide if each pair of triangles below is similar. explain your reasoning including your postulate from

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is 180°.

Step2: Calculate the third angle of the first triangle

Let the first triangle have angles 52° and 32°. Third angle = 180°-(52° + 32°)=96°.

Step3: Compare angles of the two triangles

The first triangle has angles 52°, 32°, and 96°. The second triangle has angles 96° and 32°. The third - angle of the second triangle is 180°-(96° + 32°)=52°. Since the three angles of one triangle are equal to the three angles of the other triangle, by the AA (Angle - Angle) similarity postulate, the two triangles are similar.

Answer:

The two triangles are similar because all three pairs of corresponding angles are equal (by the AA similarity postulate).