Question

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

Answer 1

Answer:

See Below.

Step-by-step 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

Answer 2

Answer:

this is your answer look it once.thank you.