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What is the proof that equiangular triangle is also called equilateral triangle?
Wiki User
∙ 11y ago
Label the triangle ABC.
Draw the bisector of angle A to meet BC at D.
Then in triangles ABD and ACD,
angle ABD = angle ACD (equiangular triangle)
angle BAD = angle CAD (AD is angle bisector)
so angle ADB = angle ACD (third angle of triangles).
Also AD is common.
So, by ASA, triangle ABD is congruent to triangle ACD
and therefore AB = AC.
By drawing the bisector of angle B, it can be shown that AB = BC.
Therefore, AB = BC = AC ie the triangle is equilateral.
Wiki User
∙ 11y ago
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The following is the answer.
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all the angles measure up to be the sameTwo segments that are both congruent to a third segment must be congruent to each otherAll of the radii of a circle are congruent
what- fill in the blank in the following proof.?
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