Question

consider the diagram.
the congruence theorem that can be used to prove $\triangle bae \cong \triangle cad$ is
\bigcirc sss.
\bigcirc asa.
\bigcirc sas.
\bigcirc hl.

Explanation:

Step1: Identify equal sides

From the diagram, we can see that \(BA = CA\) (marked as equal) and \(EA=DA\) (marked as equal).

Step2: Identify equal angle

\(\angle BAE=\angle CAD\) (they are vertical angles and vertical angles are equal).

Step3: Apply congruence theorem

Since we have two sides and the included angle of \(\triangle BAE\) equal to two sides and the included angle of \(\triangle CAD\), by the Side - Angle - Side (SAS) congruence theorem, \(\triangle BAE\cong\triangle CAD\).

Answer:

SAS.