Question

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Answer 1

Answer:

$\text{1. }\triangle IJH\cong \triangle LKM, \\\text{2. }\triangle RST\cong \triangle YXZ, \\\text{3a. Reflexive Property}, \\\text{3b. ASA (Angle-Side-Angle)}$

Step-by-step explanation:

ASA (Angle-Side-Angle) is a proof of congruence that states if two triangles share two angles and the side between those two angles, the triangles are congruent. In problems 1 and 2, the following demonstrate this:

$\text{1. }\triangle IJH\cong \triangle LKM, \\\text{2. }\triangle RST\cong \triangle YXZ$

In problem 3, $\overline{IJ}\cong \overline{IJ}$ is known in geometry as the Reflexive Property. Because of this, the two triangles in the diagram for problem 3 now share two angles and the side between them, thus they are congruent from ASA (Angle-Side-Angle).