Question

If AP bisects angle BAC and M is any point on AP, prove that the perpendiculars drawn from M to AB and AC are equal.

Answer 1

given that ,
∠2 = ∠3 ( AP is a bisector )
const .
draw M ⊥ on AP and join to AB on P and similarly in other side M ⊥ AP and join that to AC at Q .
we get ,
∠1 = ∠4 =
To prove - PM = QM
proof - in Δ APM and Δ AMQ
∠2 = ∠3 ( GIVEN )
AM = AM ( COMMON )
∠1 = ∠4 ( by const. )
by ASA Δ APM congruent to Δ AMQ .
⇒ PM = QM ( C.P.C.T)