Question

If ap bisects angle bac and m is any point on ap prove perpendicular drawn from m to ab and ac are equal

Answer 1

Answer:

let the perpendicular drawn on ab and ac be my and mz .

In triangle AYM and AZM :ASA congurency . Using c.p.c.t MY =MZ

Answer 2

From M , drawn ML such that ML is perpendicular to AB and MN perpendicular to AC

In ΔLAM and ΔMAN [AP is the bisector of ∠BAC]

ΔALM and ΔANM=90⁰ [ML⊥AB,MN⊥AC]

AM=AM [ common ]

By Angle - Angle - Side criterion of congruence ,

ΔALM≅ΔANM

The corresponding parts of the congruent triangles are congruent

ML=MN [c.p.c.t ]

Henced proved✅