Question

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

Explanation:

Step1: Analyze the given triangles

We have two right - angled triangles \(\triangle ABR\) and \(\triangle RCA\).
In right - angled triangles, the Hypotenuse - Leg (HL) congruence theorem states that if the hypotenuse and one leg of a right - angled triangle are equal to the hypotenuse and one leg of another right - angled triangle, then the two triangles are congruent.

Step2: Identify the hypotenuse and leg

From the diagram, we can assume that \(BR = CA\) (marked as equal) and \(AR=RA\) (common side, which is a leg in the right - angled triangles \(\triangle ABR\) and \(\triangle RCA\) as \(\angle BRA=\angle CAR = 90^{\circ}\)).

Answer:

HL