Question

1. which triangles are congruent by asa? △abe≅△cda △adc≅△ebc △adc≅△eda △abe≅△dea

Explanation:

Step1: Recall ASA congruence criterion

ASA (Angle - Side - Angle) 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.

Step2: Analyze the given triangles

In \(\triangle ADC\) and \(\triangle EBC\):
We know that \(\angle ADC=\angle EBC = 90^{\circ}\) (right - angles).
The side \(BC = DC\) (given by the equal - side markings).
Also, \(\angle C\) is common to both \(\triangle ADC\) and \(\triangle EBC\). So, by ASA congruence criterion \(\triangle ADC\cong\triangle EBC\).
For \(\triangle ABE\) and \(\triangle CDA\), \(\triangle ADC\) and \(\triangle EDA\), \(\triangle ABE\) and \(\triangle DEA\), we cannot prove congruence by ASA.

Answer:

\(\triangle ADC\cong\triangle EBC\)