Question

Given: WY=ZX A is the midpoint of WY. A is the midpoint of ZX. Prove: WA =ZA

Answer 1

Answer:

Given information: WY=ZX, A is the midpoint of WY and A is the midpoint of ZX.

To prove :  WA =ZA

Proof:

A is the midpoint of WY, it means A divides WY in two equal parts.

$WA=AY$

So, WY is twice of WA.

$WY=2WA$            .... (1)

A is the midpoint of ZX, it means A divides ZX in two equal parts.

$ZA=AX$

So, ZX is twice of ZA.

$ZX=2ZA$         ... (2)

$WY=ZX$                        (Given)

Substitute the values from equation (1) and (2).

$2WA=2ZA$

Divide both sides by 2.

$WA=ZA$

Hence proved.