Help with proof please? "Prove that if a triangle is equilateral than all three of its angles are congruent."

Question

thank you so much if you actually answer this question. and i don't need the whole answer, just like an idea of how to solve it

Answer 1

Just use the isosceles triangle theorem that says that if two sides of a triangle are equal then the angles opposite those sides are equal. So pick two sides and prove that the opposite angles are equal Then pick two other sides and prove that those opposite two angles are equal. Then show that all three angles must be equal becauses things equal to the same thing are equal to each other.

Answer 2

Let the original triangle be ABC, with A vertex on top, B vertex lower right. Imagine a copy of it rotated so that A is at lower right. Name it CAB, starting at the top and going clockwise. Then since triangle ABC is congruent to triangle CAB (depending on how strict your teacher is, you might have to list the 3 pairs of corresponding sides and cite SSS), angle A is congruent to angle C, angle B is congruent to angle A, and angle C is congruent to angle B by CPCTC, and with just a little transitive property of congruence you've got all 3 angles congruent to each other.

Answer 3

Any triangle that has three congruent sides also must have three congruent angles because the angle the lines need to be to connect will be the same because the sides are the same

Answer 4

Congruency is coincidence.

In an equilateral triangle the angles all HAVE to be equal. They MUST total 180°.

As such they must coincide......they must be congruent.

Answer 5

Angles opposite equal length sides are equal. This is summed up in the Law of Sines.

A/sinA = B/sinB = C/sinC

Answer 6

in geometry, an equilateral triangle is also equilangular

AAA proves, SSS

Answer 7

angle side angle ASA postulate.