Question

question 3 of 10
based only on the information given in the diagram, it is guaranteed that
△jkl ~ △wxy.

a. true
b. false

Explanation:

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

The sum of angles in a triangle is \(180^{\circ}\). In \(\triangle JKL\), one angle is \(90^{\circ}\) (right - angle) and another is \(27^{\circ}\). Let the third angle be \(\angle L\). Then \(\angle L=180^{\circ}-(90^{\circ} + 27^{\circ})=63^{\circ}\)

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

In \(\triangle WXY\), \(\angle X = 90^{\circ}\) (right - angle) and \(\angle Y=63^{\circ}\). In \(\triangle JKL\), \(\angle K = 90^{\circ}\) and \(\angle L = 63^{\circ}\). So, \(\angle K=\angle X\) (both \(90^{\circ}\)) and \(\angle L=\angle Y\) (both \(63^{\circ}\)). By the AA similarity criterion, if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

Answer:

A. True