Question

angle congruence
which congruence theorem can be used to prove (\triangle abrcong\triangle acr)?
given: (ar) bisects (angle bac), (ab = ac)
sas
sss
asa
aas

Explanation:

Step1: Analyze the given information

We know that \(AB = AC\) (given side), \(AR\) is a common side (\(AR=AR\)), and since \(AR\) bisects \(\angle BAC\), \(\angle BAR=\angle CAR\) (given angle).

Step2: Recall the SAS (Side - Angle - Side) congruence theorem

The SAS congruence theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.
In \(\triangle ABR\) and \(\triangle ACR\), we have \(AB = AC\), \(\angle BAR=\angle CAR\), and \(AR = AR\).

Answer:

SAS