Question

use a triangle congruence theorem to determine the congruent corresponding parts of the triangles. > move a choice to each space provided.
(overline{j k} cong)
(overline{m l} cong)
(angle k j m cong)
(angle j m k cong)

Explanation:

Step1: Identify congruent triangles

We have two right - angled triangles \(\triangle JMK\) and \(\triangle LMK\).
We know that \(\angle JMK=\angle LMK = 90^{\circ}\), \(\angle JKM=\angle LKM\) (given), and \(MK = MK\) (common side).
By the Angle - Angle - Side (AAS) congruence theorem, \(\triangle JMK\cong\triangle LMK\).

Step2: Find congruent corresponding parts

For congruent triangles \(\triangle JMK\cong\triangle LMK\):

• Corresponding sides:
• \(\overline{JK}\) and \(\overline{LK}\) are corresponding sides. So, \(\overline{JK}\cong\overline{LK}\).
• \(\overline{ML}\) and \(\overline{MJ}\) are corresponding sides. So, \(\overline{ML}\cong\overline{MJ}\).
• Corresponding angles:
• \(\angle KJM\) and \(\angle KLM\) are corresponding angles. So, \(\angle KJM\cong\angle KLM\).
• \(\angle JMK\) and \(\angle LMK\) are corresponding angles. So, \(\angle JMK\cong\angle LMK\).

Answer:

\(\overline{JK}\cong\overline{LK}\), \(\overline{ML}\cong\overline{MJ}\), \(\angle KJM\cong\angle KLM\), \(\angle JMK\cong\angle LMK\)