Match the reasons with the statements in the proof to prove that triangle AXC is congruent to triangle BXC, given that angles 3 and 4 are right angles and AX = BX. Given: ∠3 and ∠4 are right angles AX = BX Prove: △AXC ≅ △BXC 1. ∠3 and ∠4 are right angles Reflexive Property of Equality 2. AX = BX CX = CX Leg - Leg Theorem 3. △AXC ≅ △BXC Given

The reasons are given below.

Step-by-step explanation:

In triangle ΔAXC and ΔBXC, we are given that angles 3 and 4 are right angles and AX = BX. we have to match the reasons in the given proof of congruency of triangles △AXC ≅ △BXC

In ΔAXC and ΔBXC,

AX=BX (Given)

∠3 = ∠4 = 90° (both right angles)

CX=CX (Common i. e reflexive property of equality)

Hence by SAS similarity theorem ΔAXC ≅ ΔBXC

hence, the above are the reasons of the statements in given proof.

1.) ∠3 and ∠4 are right angles, AX = BX - - - b.) Given

2). CX = CX - - - a.) Reflexive Property of Equality

3.) △AXC ≅ △BXC - - - c.) Leg-Leg Theorem

Step-by-step explanation:

1. ∠3 and ∠4 are right angles, AX = BX

2. CX = CX

3. △AXC ≅ △BXC

a. Reflexive Property of Equality

b. Given

c. Leg-Leg Theorem