Question

1. △jkm ≅ △lkm
2. △abc ≅ △cda

use sss to explain why the triangles in each pair are congruent.
are the hypotenuse and a leg of a right triangle congruent to the hypotenuse and a leg of another right triangle?
yes
the triangles are congruent by hypotenuse - leg (hl) congruence.

Explanation:

Step1: Identify corresponding sides

In \(\triangle JKM\) and \(\triangle LKM\), \(JM = LM\) (marked with one tick), \(KM=KM\) (common side), \(JK = LK\) (marked with two ticks).

Step2: Apply SSS congruence criterion

By the Side - Side - Side (SSS) congruence criterion, if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent. Since \(JM = LM\), \(KM = KM\), \(JK=LK\), we have \(\triangle JKM\cong\triangle LKM\).

In \(\triangle ABC\) and \(\triangle CDA\), \(AB = CD\) (marked with one tick), \(BC = DA\) (marked with two ticks), \(AC=CA\) (common side).

Step3: Apply SSS congruence criterion

By the SSS congruence criterion, since \(AB = CD\), \(BC = DA\), \(AC = CA\), we have \(\triangle ABC\cong\triangle CDA\).

Answer:

1. \(\triangle JKM\cong\triangle LKM\) because \(JM = LM\), \(KM = KM\), \(JK = LK\) (by SSS).
2. \(\triangle ABC\cong\triangle CDA\) because \(AB = CD\), \(BC = DA\), \(AC = CA\) (by SSS).