Jane is asked to prove that ∠b and ∠c in the triangle represented above are congruent. It is given that AB and AC are congruent and that AD is a perpendicular bisector of BC. Her proof is shown below.

Step Statement

1 AB≅AC is given

2 D is the midpoint of BC so BD≅CD

3 AD is a shared side so AD≅AD by the reflexive property

4 ΔABD≅ΔACD

5 If ΔABD≅ΔACD then ∠b≅ ∠c

Which reason supports the statement made in step 4 of her work?

1. The angles opposite the congruent sides are congruent.

2. The sum of the interior angles in a triangle equal 180°.

3. A perpendicular bisector divides a line into two congruent segments.

4. triangles are congruent if the three sides of one triangle are congruent to three sides of the other triangle.