Question

23 what additional information is needed to prove that the triangles are congruent by sas?

Explanation:

Step1: Recall SAS congruence criterion

The Side - Angle - Side (SAS) congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Step2: Analyze the given figure

From the figure, we can see that we have one pair of congruent sides (the marked sides $\overline{RP}\cong\overline{EP}$). We need another pair of sides and the included angle between the two pairs of sides.

Step3: Determine the needed information

We need $\overline{LP}\cong\overline{KP}$ and $\angle RPL\cong\angle EPK$ (the included angles). Since the question asks for one additional piece of information assuming we can use vertical - angle property for the angles, we need $\overline{LP}\cong\overline{KP}$.

Answer:

$\overline{LP}\cong\overline{KP}$