Question

Beverly drew the line AB shown below. She then constructed line DC which is the perpendicular bisector of AB.

Answer 1

D

Line segments are congruent due to the side-angle-side congruence postulate.

Explanation:

DC is the perpendicular bisector of line AB, this mean that DC divides AB at 90 degrees into two equal parts at point E. Hence:

AE = BE

Also DE ≅ DE (reflexive property of congruence)

Also ∠AED = ∠BED = 90° (perpendicular bisector)

We can therefore say that triangle AED and triangle BED are congruent according to the side-angle-side congruence theorem. Therefore line AD = line BD