Question

Which congruence theorems can be used to prove △ABR ≅ △ACR? Check all that apply. HL SAS SSS ASA AAS

Answer 1

HL, SSS, SAS can be used to prove both triangles congruent.

Explanation:

In ΔABR And ΔACR we are given following corresponding equal parts,

∠B = ∠C = 90°

AB = AC

BR = CR

AR = AR (common)

1st. ΔABR ≅ ΔACR By HL congruence rule

as Hypotenuse AR = AR & 1 leg AB = AC or BR = CR

2nd ΔABR ≅ ΔACR By SSS congruence rule

as AB = AC & BR = CR & AR = AR (All sides of ΔABR equals to sides of ΔACR)

3rd ΔABR ≅ ΔACR By SAS congruence rule

AB = AC & ∠B = ∠C & BR = CR (2 sides of ΔABR equals to 2 sides of ΔACR and angle between both side are also equal)

ΔABR and ΔACR can not be congruent by ASA & AAS rule because no 2nd equal angle is not given.

Answer 2

HL (It's a right triangle and the hypotenuse and leg are congruent. This can also be thought of as SAS.)

SAS (Side angle side. All congruent.)

SSS (Line AR is shared by both triangles. A line is always congruent on itself. The other two are self explanatory.)

ASA and AAS cannot be used because we can only confidently confirm one angle of each triangle.