Question

tell why the two triangles are congruent. give the congruence statement. then list all other corresponding parts of the triangles that are congruent.
why are the two triangles congruent?
a. the two triangles are congruent because of the side - angle - side (sas) postulate.
b. the two triangles are congruent because of the angle - angle - side (aas) theorem.
c. the two triangles are congruent because of the angle - side - angle (asa) postulate.
d. the two triangles are congruent because of the side - side - side (sss) postulate.

Explanation:

Step1: Identify corresponding angles and sides

From the figure, we can see that \(\angle R=\angle J\), \(RT = JK\), \(\angle T=\angle K\).

Step2: Apply congruence postulate

The Angle - Side - Angle (ASA) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. Here, \(\angle R,\ RT,\angle T\) in \(\triangle SRT\) and \(\angle J,\ JK,\angle K\) in \(\triangle LJK\) satisfy the ASA condition.

Answer:

C. The two triangles are congruent because of the angle - side - angle (ASA) postulate.