Mathematics, 20.02.2020 01:36 ThetPerson
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.
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