Question

PQR is a triangle PT is a bisector of angle P and QR is extended to S. Prove that angle PQR + angle PRS = 2times angle PTR

Answer 1

GIVEN

PQR is a triangle PT is a bisector of angle P

QR is extended to S

R.T.P  :- angle PQR + angle PRS = 2 * angle PTR

∡QPT =∡RPT    [PT is a bisector of angle P]

∡PTR =∡PQR + ∡QPT

∡PQR = ∡ PTR - ∡QPT.......................[1]

∡ PRS =∡  PTR +∡  RPT....................[2]

ADDING [1] AND [2]

∡PQR+  ∡PQR = ∡  PTR - ∡QPT + ∡ PTR + ∡ RPT

∡PQR+ ∡ PQR = ∡ PTR - ∡ QPT + ∡ QPT + ∡PTR      [ ∡QPT = ∡RPT]

∡ PQR+∡ PQR =∡  PTR  +∡ PTR

∡PQR+ ∡ PQR = 2*∡ PTR  PROVED