0
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.
Still curious? Ask our experts.
Chat with our AI personalities
Professor
Steve
RafaAdd your answer:
Earn +20 pts
What is the proof that equilateral triangle is also called equiangular triangle?
Equilateral means 'same length' - Therefore if the length of each side in a triangle are the same, each angle MUST also be the same.
What are the reasons used in the proof that the equilateral triangle construction actually constructs an equilateral triangle?
The answer to this question is Two segments that are both congruent to a third segment must be congruent to each other All of the radii of a circle are congruent You're welcome.
What are reasons used to proof that the equilateral triangle construction actually constructs an equilateral triangle?
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.?
(1) equiangular, (2) division
Can the resultant of two vectors of the same magnitude be equal to the magnitude of either of the vector proof mathematically?
Yes. If the two vectors are two sides of an equilateral triangle, then the resultant is the third side and therefore equal in magnitude.
