Question

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

Explanation:

Step1: Identify the right - angled triangles

Both \(\triangle ABR\) and \(\triangle RCA\) are right - angled triangles. In \(\triangle ABR\), \(\angle BAR = 90^{\circ}\), and in \(\triangle RCA\), \(\angle ARC=90^{\circ}\)

Step2: Analyze the hypotenuse and leg

Since \(BR = CA\) (hypotenuse) and \(AR = RA\) (common leg). According to the Hypotenuse - Leg (HL) congruence theorem for right - angled triangles: If the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle, then the two right - triangles are congruent.

So, the congruence theorem that can be used to prove \(\triangle ABR\cong\triangle RCA\) is HL.

Answer:

HL