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Q.

Is it true that in a triangle, the angle bisector divides the side opposite to the angle in the ratio of the remaining sides?


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a

True

b

False 

answer is A.

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Detailed Solution

Line CE∥ Line DA (Construction) and line BE is the transversalQuestion Image∠BAD = ∠AEC [Corresponding angles] ....(1)
AD∥EC
AC is transversal
∴∠DAC = ∠ACE [Alternative angles] ...(2)
But ∠BAD = ∠DAC [Given] ...(3)
△∠AEC=∠ACE [from (1),(2) and (3)]
In △AEC side AC = side AE [Isosceles theorem] ...(4)
Now in △BCE, segAD∥segCE
BDDC=ABAE=ABAC
Hence, the given statement is true.
 
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