Question

which similarity statements are true? check all that apply
△jkl ~ △kml
△jkm ~ △jkl
△jkm ~ △kml
△jmk ~ △jkl
△jmk ~ △kml

Explanation:

Step1: Use AA (Angle - Angle) similarity criterion

In $\triangle JKL$ and $\triangle KML$:

• $\angle L=\angle L$ (common angle)
• $\angle JKL = \angle KML=90^{\circ}$

By AA similarity, $\triangle JKL\sim\triangle KML$

Step2: In $\triangle JMK$ and $\triangle JKL$

• $\angle J=\angle J$ (common angle)
• $\angle JMK=\angle JKL = 90^{\circ}$

By AA similarity, $\triangle JMK\sim\triangle JKL$

Step3: Since $\triangle JKL\sim\triangle KML$ and $\triangle JMK\sim\triangle JKL$

By transitive property (if $A\sim B$ and $B\sim C$, then $A\sim C$), $\triangle JMK\sim\triangle KML$

For $\triangle JKM-\triangle JKL$:

• $\angle JKM

eq\angle JKL$ ( $\angle JKM$ is acute and $\angle JKL = 90^{\circ}$), so $\triangle JKM$ and $\triangle JKL$ are not similar.

For $\triangle JKM-\triangle KML$:

• $\angle JKM

eq\angle KML$ ( $\angle JKM$ is acute and $\angle KML = 90^{\circ}$), so $\triangle JKM$ and $\triangle KML$ are not similar.

Answer:

• $\triangle JKL\sim\triangle KML$
• $\triangle JMK\sim\triangle JKL$
• $\triangle JMK\sim\triangle KML$