Question

alice has been asked to prove that the shaded triangles in the diagram are congruent. with one extra piece of information not shown in the diagram, alice proved the shaded triangles are congruent by sas. what could be the extra information alice used in her proof? a. ∠5≅∠6 b. ∠3≅∠4 c. ∠3≅∠2 d. ∠1≅∠2

Explanation:

Step1: Recall SAS congruence criterion

SAS (Side - Angle - Side) requires two pairs of corresponding sides to be congruent and the included angles between those sides to be congruent.

Step2: Analyze the triangles

The two shaded triangles share a common side. We need an angle between two sides of the triangles. The common side is between $\angle1$ and $\angle2$ for the two triangles. If $\angle1\cong\angle2$, along with the common side and other possible congruent sides (not shown in the problem - setup but assumed for SAS), we can prove congruence by SAS.

Answer:

D. $\angle1\cong\angle2$