Mathematics
In the given figure, P is a point in the interior of ∠ABC. If PL ⊥ BA and PM ⊥ BC such that PL = PM, prove that BP is the bisector of ∠ABC.
Triangles
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Answer
Given,
In △BLP and △BMP,
⇒ ∠L = ∠M = 90°
⇒ PL = PM [Given]
⇒ PB = PB [Common side]
∴ △BLP ≅ △BMP (By R.H.S. axiom)
⇒ ∠LBP = ∠PBM [Corresponding angles of congruent triangles are equal.]
Hence, proved that BP is the bisector of ∠ABC.
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