Question

In triangle ABC; AB = AC. P, Q and R are mid-points of sides AB, AC and BC respectively.

Prove that :
(i) PR = QR (ii) BQ = CP

Answer 1

In triangle ABC,

AB = AC

1/2AB=1/2AC
AP = AQ …….(i)[ Since P and Q are mid - points]

In TRIANGLE BCA,

PR = 1/2AC [PR is line joining the mid - points of AB and BC]

PR = AQ……..(ii)

In TRIANGLE CAB,

QR = _1/2AB[QR is line joining the mid - points of AC and BC]

QR = AP……(iii)

From (i), (ii) and (iii)

PR = QR

(ii)

AB = AC

_<B = _<C

Also,

_{1/2AB=1/2AC
BP=CQ}

In TriangleBPC and CQB,

BP = CQ

$\angle B=\angle C$

BC = BC

Therefore, $\Delta$ BPC$\Delta$ CQB [SAS]

BP = CP