01 · CORE THEOREMS
Isosceles Theorems
THEOREM 7.2
Angles Opposite to Equal Sides are Equal
In △ABC with AB = AC, draw bisector AD of ∠A meeting BC at D:
1. In △BAD and △CAD: AB = AC (given), ∠BAD = ∠CAD (construction), AD = AD (common side).
2. By SAS congruence rule, △BAD ≅ △CAD.
3. By CPCTC, ∠B = ∠C.
02 · CONVERSE THEOREM
Theorem 7.3 (Converse)
The sides opposite to equal angles of a triangle are equal. If ∠B = ∠C in △ABC, then AB = AC.