Question

In a square pqrs , diagnols bisect each other at o. prove the triangle poq congruent to triangle qop congruent to triangle ros congruent to triangle sop

Answer 1

HOPE THIS HELPS U ......

Answer 2

ΔPOQ ≅ ΔQOR ≅ ΔROS ≅ ΔSOP

Step-by-step explanation:

Given PQRS is a square.

PR and QS are diagonals bisect each other at O.

⇒ PO = OR, SO = QO

In ΔPOQ and ΔQOR,

PO = OR (given)

QO = QO (common)

∠POQ = ∠QOR (Diagonals bisect each other at 90°)

Therefore, ΔPOQ ≅ ΔQOR by SAS congruence rule. ------ (1)

Similarly,

ΔPOS ≅ ΔROS ------ (2)

ΔROS ≅ ΔQOR ------ (3)

ΔPOQ ≅ ΔSOP ------ (4)

From (1), (2), (3) and (4), we conclude that

ΔPOQ ≅ ΔQOR ≅ ΔROS ≅ ΔSOP

Hence proved.

To learn more...

1. In fig 3,PQRS is a rectangle and it's diagonal PR and QS intersect at O. if angle POQ=110°,find the measures of angle PQO angle PSQ angle ORS

https://brainly.in/question/2622833

2. In a square PQRS, diagonal PR and QS intersect at O. show that

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