Question

which congruence theorem can be used to prove ( \triangle bda cong \triangle bdc )?
hl
ssa
aas
sss

Explanation:

Step1: Analyze the given information

We know that \(BD = BD\) (common side). Also, from the figure, \(BA=BC\) (given as equal segments) and \(AD = CD\) (given as equal segments).

Step2: Recall the SSS congruence theorem

The SSS (Side - Side - Side) congruence theorem states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.
In \(\triangle BDA\) and \(\triangle BDC\), we have \(BA = BC\), \(AD=CD\) and \(BD = BD\).

Answer:

SSS