Question

In quadrilateral PRQS , PR = PS and PQ bisects.

Show that ∆ PQR ~ ∆ PQS

What can you say about QR and QS.​

Answer 1

Answer:

In ∆PQR and ∆PQS,

PR = PS. (Given)

L QPR = L QPS. (PQ bisects)

PQ = PQ. (Common)

:. ∆PQR = ∆PQS {By SAS Congruency rule}

=> QR = QS [CPCT]

Hence, proved.

Answer 2

$\huge\mathbb\red{SOLUTION~:-}$

$\huge\bold\green{Given~:-}$

In Quadrilateral PRQS

PR = PS

PQ bisects angle P

$\huge\boxed{\fcolorbox{cyan}{yellow}{angle~RPQ~=~angle~SPQ}}$ → (1)

$\huge\bold\green{Required~to~proof~:-}$

∆ PQR ~ ∆ PQS

$\huge\bold\green{Proof~:-}$

From ∆ PQR and ∆ PQS

PR = PS $\huge\orange{[:.given]}$

angle RPQ = angle SPQ $\huge\orange{[:.from~equation~(1)~given]}$

PQ = PQ $\huge\orange{[:.Common~side]}$

By SAS congruency rule

∆ PQR ~ ∆ PQS

:. The corresponding parts of congruent traingles are equal .

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[ NOTE :- Mate your diagram is ABCD but according to your question I answered PQRS ]