Question

what is the property of angle bisector​

Answer 1

Answer:

Step-by-step explanation:

The bisector of an angle of a triangle divides the side opposite to the angle in the ratio of the remaining sides.

Given:​ 

In ∆ ABC , side AD bisects Angle BAC such that B - D - C.

 

Construction :

Draw seg DE perpendicular to side AB and seg DN perpendicular to side AC.

Proof :

Point D lies on the bisector of Angle BAC

By angle bisector Theorem, DE = DF ... (1)

Now,

Ratio of areas of the two triangles is equal to the ratio of the products of their bases and corresponding heights.

From 1, 

Also,∆ADB and ∆ADC have common vertex A 

and their bases BD and DC lie on the same line BC. So their heights are equal.

Area of triangles with equal heights are proportional to their corresponding bases.

From 2 and 3 ,

We get 

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Answer 2

Step-by-step explanation:

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