SOLUTION: the corollary to theorem 4.7 states, "if a triangle is equiangular then it is equiladeral." Write a proof of this corollary.

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Question 166901This question is from textbook geometry
: the corollary to theorem 4.7 states, "if a triangle is equiangular then it is equiladeral." Write a proof of this corollary. This question is from textbook geometry

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
triangle ABC using (=) to mean congruent
1.angle A(=)angle B(=)angle C...........1. given
2 if angle A(=)angle B then AC(=)BC.....2. converse of base angle theorem
if angle B(=)angle C then AC(=)AB
3. since AC(=)BC and AC(=)AB............3. transitive
then BC(=)AB
4. All sides are equal.therefore......... 4. definition of an equilateral tri
this is an equilateral triangle.