Question

PQRS is a quadrilateral such that diagonal PR bisects angle P and angle R.
Prove that PQ = PS and RS = RQ.​

Answer 1

Answer:

Given:

PQRS is a quadrilateral, diagonal PR bisects angle P and angle R.

To prove:

PQ = PS and RS = RQ.

Step-by-step explanation:

In ️triangle PQR & triangle ️PSR;

(A) angle QPR= angle RPR(since diagonal PR bisects angle P)

(S) Side PR=PR(common side)

(A) angle QRP= angle SRP(since diagonal PR bisects angle R)

therefore, triangle ️PQR is congruent to️ triangle PSR by ASA congruence rule.

=》side PQ= PS and RS = RQ.( by C.P.C.T.)

Hence proved.

Answer 2

Question :

PQRS is a quadrilateral such that diagonal PR bisects angle P and angle R. Prove that PQ = PS and RS = RQ.

Given :

PQRS is a quadrilateral, diagonal PR bisects angle P and angle R.

To prove :

PQ = PS and RS = RQ.

Solution :

In ️triangle PQR & triangle ️PSR;

(A) angle QPR= angle RPR(since diagonal PR bisects angle P)

(S) Side PR=PR(common side)

(A) angle QRP= angle SRP(since diagonal PR bisects angle R)

Therefore, Δ️PQR is congruent to️ ΔPSR by ASA congruence rule.

=》side PQ= PS and RS = RQ.( by C.P.C.T.)

Hence proved.

Additional Information :

ASA congruency means Angle Side Angle. In this rule, we have to make two angles and one side equal.

Thank you.