Question

consider the diagram.
which congruence theorem can be used to prove ( \triangle abr cong \triangle rca )?
asa
sss
sas
hl

Explanation:

Step1: Identify right angles

In \(\triangle ABR\) and \(\triangle RCA\), \(\angle RAB=\angle ARC = 90^{\circ}\) (given right - angle markings).

Step2: Identify common side

\(RA = AR\) (common side in both triangles).

Step3: Identify equal sides

From the diagram, \(BR=CA\) (marked as equal).
Since we have two right - angled triangles (\(\angle RAB=\angle ARC = 90^{\circ}\)), the hypotenuse (\(BR = CA\)) and a leg (\(RA=AR\)) are equal.

Answer:

HL (Hypotenuse - Leg) congruence theorem.