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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
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Equilateral triangles must also be?
equiangular.
Can a equiangular triangle be an equilateral triangle?
Every equilateral triangle is equiangular, and every equiangular triangle is equilateral.
Which two words describe all equiangular triangles?
equilateral and similar
Is a triangle a small regular polygon?
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).
When is an equilateral triangle not equiangular?
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.
