Question

question 5 of 10
based only on the information given in the diagram, it is guaranteed that
△abc ~ △xyz
a. true
b. false

Explanation:

To determine if \(\triangle ABC \sim \triangle XYZ\), we use the AA (Angle - Angle) similarity criterion. In \(\triangle ABC\) and \(\triangle XYZ\):

• Both triangles are right - angled, so \(\angle C=\angle Z = 90^{\circ}\).
• We are given that \(\angle A=\angle X = 43^{\circ}\).

By the AA similarity postulate, if two angles of one triangle are equal to two angles of another triangle, the triangles are similar. Since two angles (\(90^{\circ}\) and \(43^{\circ}\)) of \(\triangle ABC\) are equal to two angles of \(\triangle XYZ\), \(\triangle ABC\sim\triangle XYZ\) is guaranteed.

Answer:

A. True