Question

Given: WY=ZX

A is the midpoint of WY.

A is the midpoint of ZX.

Prove: WA =ZA

Answer 1

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.