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