Question

1. In Figure 1, PL is right angle on AB and PM is right angle on BC such that PL = PM.
Show that P lies on the bisector of angle ABC.

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Answer 1

Answer:

We have,

∠1=∠2     [∵ BP is the bisector of ∠ABC]

∠1=∠2     [∵ BP is the bisector of ∠ABC]∠1=∠3     [∵PQ∥BA]

∠1=∠2     [∵ BP is the bisector of ∠ABC]∠1=∠3     [∵PQ∥BA]∴∠2=∠3

∠1=∠2     [∵ BP is the bisector of ∠ABC]∠1=∠3     [∵PQ∥BA]∴∠2=∠3⇒PQ=BQ

∠1=∠2     [∵ BP is the bisector of ∠ABC]∠1=∠3     [∵PQ∥BA]∴∠2=∠3⇒PQ=BQ⇒ΔPBQ is isosceles