Question

PQRS is a kite with PQ = PS and RS=RQ Prove that the figure formed by joining the mid-points of the consecutive sides rectangle. ​

Answer 1

☯ Given: In quadrilateral PQRS, PQ = PS  and RQ = RS.

☯ To prove: ∠PQR = ∠PSR

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀

❒ 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

   

$\therefore \pink{\sf{\underline{Proved \; that \;\angle PQR = \angle PSR.}}}$

Answer 2

Answer:

$\huge \underline \bold \red{answer}$

☯ Given: In quadrilateral PQRS, PQ = PS and RQ = RS.

☯ To prove: ∠PQR = ∠PSR

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀

❒ 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