Best Answer

Statement Reason

1. triangle ABC is equilateral..............................................given

2. AC is congruent to BC;

AB is congruent to AC........................................definition of equilateral

3. angle A is congruent to angle B;

and B is congruent to angle C.............................Isosceles Theorem

4. angle A is congruent to angle C..................Transitive Property of Congruence

5. triangle ABC is equiangular...............................Definition of equiangular

Q: Prove that equilateral triangles are equiangular?

Write your answer...

Submit

Still have questions?

Continue Learning about Math & Arithmetic

equiangular.

Every equilateral triangle is equiangular, and every equiangular triangle is equilateral.

equilateral and similar

A regular polygon is any polygon that has sides which are the same length and angles whose measures are equal. An equilateral triangle (also equiangular triangle) is a regular polygon. Other isosceles triangles (equilateral triangles are isosceles, but they are an exception) and scalene triangles are not regular polygons. A side note: Only in a triangle is a polygon regular solely if it is equilateral. (Since an equilateral triangle is equiangular as well). This is NOT always true in other polygons, like quadrilaterals, where it can be equilateral but not necessarily equiangular (a rhombus) or equiangular but not equilateral (a rectangle).

If a triangle is equiangular, it will have all equal angles. So, it might be similar to another equiangular triangle, but not congruent. It is not equilateral if the sides are not equal in length. All equiangular triangles are similar, but not all of them are congruent, which means they do not all have corresponding side lengths. But, all equilateral triangles are equiangular.

Related questions

Are equiangular hexagons equilateral? Image result for An equiangular hexagon that is not a=equilateral? Equiangular hexagons An equilateral hexagon with 1:2 edge length ratios, with equilateral triangles. This is spirolateral 2120°.

There are many polygons that are both equiangular and equilateral. For example, squares and equilateral triangles are both equiangular and equilateral polygons. The general term for polygons that are both equiangular and equilateral is regular.

equiangular.

Every equilateral triangle is equiangular, and every equiangular triangle is equilateral.

Equiangular triangle are also the equilateral triangles. These have equal angles and equal sides.

an equiangular triangle (and by definition, equilateral triangles are always equiangular too)

Yes, all the angles of an equilateral triangle are always 60 degrees.

equilateral and similar

A regular polygon is any polygon that has sides which are the same length and angles whose measures are equal. An equilateral triangle (also equiangular triangle) is a regular polygon. Other isosceles triangles (equilateral triangles are isosceles, but they are an exception) and scalene triangles are not regular polygons. A side note: Only in a triangle is a polygon regular solely if it is equilateral. (Since an equilateral triangle is equiangular as well). This is NOT always true in other polygons, like quadrilaterals, where it can be equilateral but not necessarily equiangular (a rhombus) or equiangular but not equilateral (a rectangle).

If a triangle is equiangular, it will have all equal angles. So, it might be similar to another equiangular triangle, but not congruent. It is not equilateral if the sides are not equal in length. All equiangular triangles are similar, but not all of them are congruent, which means they do not all have corresponding side lengths. But, all equilateral triangles are equiangular.

Equilateral triangles are also equiangular.

No, an equilateral triangle has to be equiangular, but an equiangular triangle does NOT have to be equilateral