Question

in a quadrilateral pqrs,to bisects angle R and RQ=RS. prove that (i) PQ=PS,(ii) RP is the perpendicular ​

Answer 1

Answer:

. In the kite shown, PQ = PS and ∠QPR = ∠SPR.

(i) Find the third pair of corresponding parts to make ∆ PQR ≅ ∆PSR by SAS congruence condition.

(ii) Is ∠QRP = ∠SRP?

Solution:

(i) In ∆ PQR and ∆ PSR

PQ = PS → given

∠QPR = ∠SPR → given

PR = PR → common

Therefore, ∆PQR ≅ ∆PSR by SAS congruence condition

(ii) Yes, ∠QRP = ∠SRP (corresponding parts of congruence triangle).

Step-by-step explanation:

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