Question

Which of the following are reasons used in proof that the angle bisector construction can be used to bisect any angle

Answer 1

In the construction we use the fact that all radius of a circle are congruent, so AB ≅ AC, as both segments are radius of the same circle.

In the same way, this let us write:

`BD\cong CD`

As, by reflexive property, we can write AD ≅ AD.

Then, we have triangles with 3 pairs of congruent sides, so they are congruent by the SSS postulate.

Then, because of CPCTC (corresponding parts of congruent triangles are congruent), the angle BAD is congruent to angle CAD, meaning that AD is a bisector of angle BAC.

Answer: Options A, C and D.