Question

practice with congruency theorems and cpctc. which congruency theorem can be used to prove that △abd ≅ △dca? sss asa sas aas

Explanation:

Step1: Identify the given information

From the figure, we have \(AB = DC\) (marked as equal), \(\angle BAD=\angle CDA = 90^{\circ}\), and \(AD = DA\) (common side).

Step2: Recall the congruency theorems

• SSS (Side - Side - Side): Requires three pairs of equal sides. Here we have two sides and an included angle.
• ASA (Angle - Side - Angle): Requires two angles and the included side.
• SAS (Side - Angle - Side): Requires two sides and the included angle. We have \(AB = DC\), \(\angle BAD=\angle CDA\), and \(AD = DA\).
• AAS (Angle - Angle - Side): Requires two angles and a non - included side.

Answer:

SAS