Question

If the angular bisector of an angle of a triangle bisects the opposite side , prove that the triangle is an isosceles triangle.

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Answer 1

this is your answer look it once.thank you.

Answer 2

See Below.

Explanation:

Please refer to the attachment below.

In order to complete the proof, we create a new segment DE that extends from D and is equal to AD. The endpoint of DE will be connected to B.

Statements: Reasons:

`1)\text{ } AD\text{ bisects } CB` Given

`2)\text{ } CD=DB` Definition of Bisector

`3)\text{ } AE=DE` Given

`4)\text{ } \angle ADC \cong \angle EDB` Vertical Angles are Congruent

`5)\text{ } \Delta ADC\cong \Delta EDB` SAS Congruence

`6)\text{ } \angle BED\cong \angle CAD` CPCTC

`7)\text{ } AD\text{ bisects } \angle A` Given

`8)\text{ } \angle CAD\cong \angle BAD` Definition of Congruence

`9)\text{ } \angle BED\cong\angle BAD` Substitute

`10)\text{ } BE=BA` Isosceles Triangle Theorem

`11) \text{ } BE=CA` CPCTC

`12)\text{ } CA=BA` Substitute

`13)\text{ } \Delta ABC\text{ is isosceles}` Isosceles Triangle Definition