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  

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.