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A DeltaABC is right angled at A and L is...

A `DeltaABC` is right angled at A and L is a point on BC such that `ALbotBC`. Prove that `angleBAL=angleACB`.

Text Solution

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We know that in a right-angled trianlge, the sum of the two acute anlges is `90^(@)`.
So, in right trianlge `DeltaALB`, we have
`angleBAL+angleABL+=90^(@)impliesangleBAL+angleABC=90^(@)" "......(i)`
In right triangle BAC, we have
`angleABC+angleACB=90^(@)." "....(ii)`
From (i) and (ii), we get
`angleBAL+angleABC=angleABC+angleACB`.
Hence, `angleBAL+angleACB`.
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