Question

pqrs is a quadrilateral in which PS equal to Q R and angle qps equal to angle pqr prove that (i) triangle pqs congruent to triangle QPR (ii) p r = qs (iii) angle QPR equals to angle ppqs


answer fast....

Answer 1

Given:

PQRS is a quadrilateral

PS = PQ

∠QPS = ∠PQR

To find:

Prove that

(i) Δ PQS is congruent to Δ QPR

(ii) PR = QS

(iii) ∠QPR equals to ∠PQS

Solution:

(i) Proving triangle PQS is congruent to triangle QPR:

In Δ PQS and Δ QPR, we have

PS = QR ...... (given)

∠QPS = ∠PQR ..... (given)

PQ = PQ ...... (common side to both the triangles)

∴ Δ PQS ≅ Δ QPR ...... By SAS Congruency

Hence proved

(ii) Proving PR = QS:

We know that → when two triangles are congruent to each other then their corresponding sides are equal in length.

Here

Δ PQS ≅ Δ QPR

and

PR & QS are the corresponding sides of the two congruent triangles

∴ PR = QS

Hence proved

(iii) Proving ∠QPR = ∠PQS:

We know that → when two triangles are congruent to each other then their corresponding angles will have the same measurement.

Here

Δ PQS ≅ Δ QPR

and

∠QPR & ∠PQS are the corresponding angles of the two congruent triangles

∴ ∠QPR = ∠PQS

Hence proved

---------------------------------------------------------------------------------------

Also View:

Quadrilateral PQRS, PQ=PS and RQ=RS, prove that angle PQR = angle PSR​?

https://brainly.in/question/15484927

In the figure, = QR /QS = QT/PR and ∠1 = ∠ 2 then prove that ∆PQS ~ ∆TQR

https://brainly.in/question/3084770

In quadrilateral PQRS, PQ = PS and PR bisects angleP.  Show that trianglePRQ congruent to triangle PRS.  What can you say about QR and SR?

https://brainly.in/question/10132798

Answer 2

HEY...HOPE IT HELPS...PLEASE MARK AS THE BRAINLIEST...