Question

In a kite PQRS , PQ = PS, RQ = RS.If ∆P = 45° and ∆R = 55°, find ∆ Q and ∆ S.​

Answer 1

$\huge \fbox \purple{❥ Answer}$

Proved ∠PQR = ∠PSR.

To prove : ∠PQR = ∠PSR

Given :

Quadrilateral PQRS.

PQ = PS

RQ = RS

Proof :

From the figure,      

In quadrilateral PQRS,

Given that ⇒ PQ = PS

Common side ⇒ PR = PR

Given that ⇒ RQ = RS

By SSS (Side - Side - Side) test,

ΔPQR ≅ ΔPSR

Then, the corresponding angles of congruent triangle

∠PQR = ∠PSR

Hence, proved that ∠PQR = ∠PSR.

To learn more...

1. In quadrilateral PQRS, PQ = PS and PR bisects angleP.

Show that trianglePRQ congruent to triangle PRS.

What can you say about QR and SR?

brainly.in/question/10132798

2. PQRS is a kite in which PQ=PS and QR=SR.Show that PR is the perpendicular bisector of diagonal QS.

brainly.in/question/987102

Answer 2

Proved ∠PQR = ∠PSR.

To prove : ∠PQR = ∠PSR

Given :

Quadrilateral PQRS.

PQ = PS

RQ = RS

Proof :

From the figure,

In quadrilateral PQRS,

Given that ⇒ PQ = PS

Common side ⇒ PR = PR

Given that ⇒ RQ = RS

By SSS (Side - Side - Side) test,

ΔPQR ≅ ΔPSR

Then, the corresponding angles of congruent triangle

∠PQR = ∠PSR

Hence, proved that ∠PQR = ∠PSR.