Question 252915: explain why it is necessary for two congruent angles to be in the same triangle in order for the sides opposite them to be congruent Answer by drk(1908) (Show Source):
You can put this solution on YOUR website! This seems like an explanation of the isosceles triangle theorem.
THEOREM 1: If two angles of a triangle are congruent then their opposite sides are congruent.
THEOREM 2: If two sides of a triangle are congruent then their opposite angles are congruent.
--
THEOREM 1:
given: two angles of a triangle are congruent.
prove: opposite sides of the triangle are congruent.
STATEMENT 1: triangle ABC
REASON 1 : given
STATEMENT 2: angle B congruent angle C.
REASON 2: given
STATEMENT 3: construct ray AD such that it is an altitude of triangle ABC.
REASON 3: definition of construction.
STATEMENT 4: angles BDA and CDA are right angles
REASON 4: definition of altitude.
STATEMENT 5: AD congruent AD
REASON 5: reflexive property of equality.
STATEMENT 6: triangle BDA congruent triangle CDA
REASON 6: AAS postulate
STATEMENT 7: AB congruent AC
REASON 7: CPCTC.
--
The proof of THEOREM 2 will be similar.
hope that helps.
(