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What is the proof that equilateral triangle is also called equiangular triangle?

Anonymous

∙ 14y ago

Updated: 12/8/2022

Equilateral means 'same length' - Therefore if the length of each side in a triangle are the same, each angle MUST also be the same.

Wiki User

∙ 14y ago

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Q: What is the proof that equilateral triangle is also called equiangular triangle?

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What is the proof that equiangular triangle is also called equilateral triangle?

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.

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.

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Related Questions

What are reasons used in the proof that the equilateral triangle construction actually constructs an equilateral triangle triangle?

The following is the answer.

What is the proof that equiangular triangle is also called equilateral triangle?

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.

Are reasons used in the proof that the equilateral triangle construction actually constructs an equilateral triangle Check all that apply.?

An equilateral triangle is a regular polygon because it has 3 equal sides and 3 equal 60 degree angles that add up to 180 degrees.

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

what- fill in the blanks in the following paragraph proof?

(1) equiangular, (2) division

What is the area of an equilateral triangle with sides of 10 inches and height of 7 inches?

I'm showing it with absolute proof. Equilateral triangle both side are same in size & same angel.It's given with the sides of 10 inches & height 7 inches. I don't need to count the height(7),just use side(10).The formula is=Area of a equilateral triangle="root over of 3" /4 * "a square"Now I use this formula,where "a" is 10. So the answers come=43.3,which is 44.So the Correct answer is=44 inches.* * * * *Mostly correct, but:43.3 should be rounded to 43, not 44.The units for the area should be square inches, not inches.

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.

What is the proof showing that the heights of a triangle are concurrent?

There cannot be a proof because the statement need not be true.

complete the paragraph proof?

converse of the isosceles triangle theorem

which completes the paragraph proof?

converse of the isosceles triangle theorem

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