In triangle PQR, PS is the bisector of angle QPR and PT perpendicular QR. Show that angle TPS = 1/2 (angle Q-angle R).
Its urgent ...Answer Fast Please.....
given :PS is the bisector
PT is perpendicular
to prove : TPS = 1/2 (Q-R)
solution : angle qps = angle rps
angle qpt + angle tps = angle spr
in triangle prt,
angle ptq = 900
angle qpt + angle qpt = 900
angle q + 900 - angle qpt
in triangle prt,
angle ptr = 900
angle r + angle tpr +900
angle r + (angle tps + angle spr) - angle qpt
angle q - angle r = angle tps + (angle spr - angle qpt)
angle q - angle r = angle tps + angle tps
angle tps = 1/2 (angle q - angle r)