Question

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

Answer 1

Answer:

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  

Answer 2

Answer:

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.