1.

In adjacent figure, PR > PQ and PS bisects ∠QPR. Prove that ∠PSR > ∠PSQ.

Answer»

GIVEN:

PR > PQ & PS bisects ∠QPR

To PROVE:

∠PSR > ∠PSQ

Proof:

∠PQR > ∠PRQ — (i) (PR > PQ as angle opposite to larger side is larger.)


∠QPS = ∠RPS — (ii) (PS bisects ∠QPR)


∠PSR = ∠PQR +∠QPS — (iii)

(exterior angle of a triangle EQUALS to the sum of opposite interior angles)


∠PSQ = ∠PRQ + ∠RPS — (iv)

(exterior angle of a triangle equals to the sum of opposite interior angles)


Adding (i) and (ii)

∠PQR + ∠QPS > ∠PRQ + ∠RPS

∠PSR > ∠PSQ [from (i), (ii), (iii) and (iv)]


Hope this will help you.......


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