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Perpendicular Lines

P is a point ...

Question

P is a point equidistant from the two lines l and m intersecting at a point A . Show that AP bisects the angle between them

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P

l

m

A

A P

^{'} P^{'}

^{'} l^{'}

^{'} m^{'}

^{'} A^{'}

A P

P

l

m

A

△ P A B ≅ △ P A C

The given figure shows a triangle ABC in whcih AD bisects angle BAC. EG is perpendicular bisector of side AB which intersects AD at point F.

Prove that:

(i) F is equidistant from A and B.

(ii) F is equidistant from AB and AC.

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