Question

NEED HELP ASAP PLEASE!! 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.

Answer 1

Answer: The proof is mentioned below.

Explanation:

Here, Δ ABC is isosceles triangle.

Therefore, AB = BC

Prove: Δ ABO ≅ Δ ACO

In Δ ABO and Δ ACO,

∠ BAO ≅ ∠ CAO ( AO bisects ∠ BAC )

∠ AOB ≅ ∠ AOC ( AO is perpendicular to BC )

BO ≅ OC ( O is the mid point of BC)

Thus, By ASA postulate of congruence,

Δ ABO ≅ Δ ACO

Therefore, By CPCTC,

∠B ≅ ∠ C

Where ∠ B and ∠ C are the base angles of Δ ABC.