Question

solve each exercise. then rate your understanding of the success criteria in your journal.

1. identifying similar triangles

tell whether the triangles are
similar. explain.

Explanation:

Step1: Find the third angle of the first triangle

The sum of angles in a triangle is \(180^{\circ}\). Let the third angle of the first triangle be \(x\). Then \(x + 63^{\circ}+63^{\circ}=180^{\circ}\), so \(x = 180^{\circ}- 63^{\circ}-63^{\circ}=54^{\circ}\).

Step2: Check the AA (Angle - Angle) similarity criterion

The first triangle has angles \(54^{\circ},63^{\circ},63^{\circ}\). The second triangle has two angles \(63^{\circ},63^{\circ}\). By the AA similarity criterion (if two angles of one triangle are equal to two angles of another triangle, the triangles are similar), since two angles (\(63^{\circ}\) and \(63^{\circ}\)) of the first triangle are equal to two angles (\(63^{\circ}\) and \(63^{\circ}\)) of the second triangle.

Answer:

The triangles are similar.