Question

Given: Q is the midpoint of PR. QR=QS
Prove: QS+QR=PR

Answer 1

QR + QS

=
`(1)/(2) PR + (1)/(2) PR`

`= PR ((1)/(2) + (1)/(2) ) = PR` (hence proved)

Explanation:

As shown in figure below:

Given: Q is the midpoint of PR. and QR = QS

Sol: Since Q is the midpoint of PR. ∴
`QR = (1)/(2) PR`

Now QR = QS (Given)

∴
`QS = (1)/(2) PR`

Now, QR + QS

=
`(1)/(2) PR + (1)/(2) PR`

`= PR ((1)/(2) + (1)/(2) ) = PR`

So, OR + QS = PR (hence proved)