Question

for items 11 - 13, refer to the diagram. if ∠bac≅∠dca, is △abe≅△cde? explain. a yes, the triangles are congruent by angle - angle - side. b yes, the triangles are congruent by side - side - side. c yes, the triangles are congruent by side - angle - side. d no, the triangles are not congruent.

Explanation:

Step1: Identify vertical angles

$\angle AEB=\angle DEC$ (vertical - angles are equal).

Step2: Given angle equality

We are given that $\angle BAC=\angle DCA$.

Step3: Identify equal sides

From the diagram, $AB = CD$ (the marked equal - sides).

Step4: Apply Angle - Angle - Side (AAS) congruence criterion

In $\triangle ABE$ and $\triangle CDE$, we have $\angle BAC=\angle DCA$, $\angle AEB=\angle DEC$, and $AB = CD$. So, $\triangle ABE\cong\triangle CDE$ by Angle - Angle - Side congruence.

Answer:

A. Yes, the triangles are congruent by Angle - Angle - Side.