Question

The provided diagram of triangle ABC will help you to prove that the base angles of an isosceles triangle are congruent. The first step is to draw auxiliary line AO. What must be true about  in order to complete the proof using the ASA (Angle Side Angle) triangle congruency theorem? Classify each statement as needed or not needed to complete the proof. bisects  BAC needednot needed is perpendicular to  needednot neededPoint O is the midpoint of  needednot needed is an altitude. needednot needed

Answer 1

AO bisects BAC. Needed

AO is perpendicular to BC. Needed.

Point O is the midpoint. Not needed.

AO is the altitude. Not needed

Explanation:

ASA Congruence Theorem:

Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other triangle.

In this question:

Triangles AOB and AOC.

For them to have two equal angles:

We need for AO bisecting BAC, so OB = OC

If AO bisects BAC, we also have that AO is perpendicular to BC.

Point O being the midpoint and AO being the altitude are not needed, we only need the angles, not the dimensions.