Question

In the given figure, PQ = RS and Angle PQR = Angle QRS.
Prove That
(i) PR = QS
(ii) QO= OR​

Answer 1

i) congruent /\ PQR & /\ SRQ

THEN PROVE PR=QS BY CPCT

Answer 2

Answer:

In the given figure, PQ=RS and ∠PQR=∠QRS then it is proved that

(i) PR = QS and (ii) QO = OR.

Step-by-step explanation:

We have a figure in which PQ = RS and ∠PQR = ∠QRS and we need to prove that

(i) PR = QS and (ii) QO = OR

Step 1 of 2

Let us see the ΔPQR and ΔSRQ in which

PQ = RS      ....(1)

QR = QR     ......(2)

and ∠PQR = ∠SRQ   .....(3)

Then by applying the Side Angle Side property to these triangle we get

ΔPQR ≅ SRQ

It means both triangles are concruent.

Hence PR = QS

Step 2 of 2

Again let us see ΔPQO = ΔSRO

PQ = SR      (Given)

∠POQ = ∠SOR    (Vertically opposite Angle)

∠QPO = ∠RSO     (As ΔPQR ≅ SRQ )

Then by appllying the Angle Angle Side Congruency to these triangles we get

ΔPQO ≅ SRO

It means both triangles are concruent.

Hence QO = OR

Hence it is proved that (i) PR = QS and (ii) QO = OR