Question

consider the diagram.
which congruence theorem can be used to prove
△abr ≅ △rca?
hl
sss
asa
sas

Explanation:

Step1: Identify the triangles' properties

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: Check the given equal parts

From the diagram, we can see that the hypotenuses \(BR\) and \(AC\) are equal (marked with the same symbol), and the legs \(AR\) is common (reflexive property, \(AR = AR\)).

Answer:

HL