Question

consider the diagram. the congruence theorem that can be used to prove △bae ≅ △cad is sss. asa. sas. hl.

Explanation:

Step1: Analyze the given information

From the diagram, we can see that \( \angle BAE=\angle CAD = 90^{\circ}\) (right angles). Also, \(BA = CA\) (marked as equal) and \(EA=DA\) (marked as equal).

Step2: Recall the congruence theorems

• SSS (Side - Side - Side): Requires three pairs of equal sides. Here we have two pairs of sides and an included angle.
• ASA (Angle - Side - Angle): Requires two angles and the included side. We have two sides and an included angle.
• SAS (Side - Angle - Side): Requires two sides and the included angle. In \(\triangle BAE\) and \(\triangle CAD\), \(BA = CA\), \(\angle BAE=\angle CAD\), and \(EA = DA\).
• HL (Hypotenuse - Leg): Applies only to right - angled triangles for congruence when hypotenuse and one leg are equal. But here we are not using the hypotenuse - leg relationship.

Answer:

SAS.