Question

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

Explanation:

Step1: Recall the AA (Angle - Angle) similarity criterion

Two right - angled triangles are similar if they have one common acute angle.

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

• \(\angle JMK=\angle KML = 90^{\circ}\)
• \(\angle JKM\) is common to both \(\triangle JKM\) and \(\triangle KML\)

So, by AA similarity criterion \(\triangle JKM\sim\triangle KML\)

Step3: Analyze \(\triangle JMK\) and \(\triangle JKL\)

• \(\angle JMK=\angle JKL = 90^{\circ}\)
• \(\angle J\) is common to both \(\triangle JMK\) and \(\triangle JKL\)

So, by AA similarity criterion \(\triangle JMK\sim\triangle JKL\)

Answer:

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