Question

complete the statement below about the two figures. they are not similar because their corresponding angles are not congruent. image of two triangles: triangle abc with angles at b: 81°, at a: 67°, at c: 32°; triangle xyz with angles at y: 66°, at x: 59°, at z: 55°

Explanation:

Step1: Calculate the third angle of triangle \(ABC\)

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle ABC\), if \(\angle B = 81^{\circ}\) and \(\angle A=67^{\circ}\), then \(\angle C=180^{\circ}-(81^{\circ} + 67^{\circ})=180^{\circ}-148^{\circ}=32^{\circ}\).

Step2: Check angle - angle similarity

For \(\triangle XYZ\), the angles are \(55^{\circ}\), \(59^{\circ}\), and \(66^{\circ}\). For \(\triangle ABC\), the angles are \(32^{\circ}\), \(67^{\circ}\), and \(81^{\circ}\). Since there is no correspondence of two (or three) equal angles between the two triangles (e.g., \(32^{\circ}
eq55^{\circ}
eq59^{\circ}
eq66^{\circ}
eq67^{\circ}
eq81^{\circ}\)), by the AA (angle - angle) similarity criterion (which states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar), the two triangles are not similar.

Answer:

They are not similar because their corresponding angles are not congruent.