Question

which similarity statements are true? check all that apply.

□ △jkl ~ △kml

□ △jkm ~ △jkl

□ △jkm ~ △kml

□ △jmk ~ △jkl

□ △jmk ~ △kml

Explanation:

Step1: Recall AA (Angle - Angle) similarity criterion

If two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

Step2: Analyze \(\triangle JKL\) and \(\triangle KML\)

In \(\triangle JKL\) and \(\triangle KML\), \(\angle L=\angle L\) (common angle) and \(\angle JKL = \angle KML=90^{\circ}\). By AA similarity, \(\triangle JKL\sim\triangle KML\)

Step3: Analyze \(\triangle JKM\) and \(\triangle KML\)

In \(\triangle JKM\) and \(\triangle KML\), \(\angle JMK=\angle KML = 90^{\circ}\). Also, \(\angle J+\angle JKM = 90^{\circ}\) and \(\angle JKM+\angle MKL=90^{\circ}\), so \(\angle J=\angle MKL\). By AA similarity, \(\triangle JKM\sim\triangle KML\)

Step4: Analyze \(\triangle JMK\) and \(\triangle JKL\)

In \(\triangle JMK\) and \(\triangle JKL\), \(\angle J=\angle J\) (common angle) and \(\angle JMK=\angle JKL = 90^{\circ}\). By AA similarity, \(\triangle JMK\sim\triangle JKL\)

Answer:

\(\triangle JKL\sim\triangle KML\), \(\triangle JKM\sim\triangle KML\), \(\triangle JMK\sim\triangle JKL\)