0
Yes, the angles at the vertices are each 60 degrees (total 180 degrees, as do the sum of the angles in all triangles).
The Law of Sines (see related link) can be used to show this:
a/sin(A) = b/sin(B) = c/sin(C), where a,b,c are the side lengths, and A,B,C are the angles (opposite of sides a,b,c respectively).
Since a = b = c for equilateral, then sin(A) = sin(B) = sin(C). Now you can have two different angles which give the same sine, say for example if A=80°, and B=100°, then sin(80°) = sin(100°), but then because they must add to 180°, then angle C must be 0°, so it's not a triangle anymore, so A and B must be equal, then in the same way it can be shown that C must also equal A and B. Since all three angles are equal, and they must add to 180°, then the angle equals 180° / 3 = 60°.
Note that for any angle x, the other angle which has the same sine is [180° - x].
This means, of course, that every equilateral triangle, is simply a smaller or larger version of every other equilateral triangle (they are similar).
Add your answer:
Earn +20 pts
Does a equiangular triangle have to be equilateral?
No, an equilateral triangle has to be equiangular, but an equiangular triangle does NOT have to be equilateral
Can an equilateral triangle can be equiangular?
It always is because it has 3 equal angles of 60 degrees
What type of triangle is always an equiangular triangle?
An equilateral triangle.
A type of triangle with congruent angles?
an equiangular triangle (and by definition, equilateral triangles are always equiangular too)
Can a equiangular triangle be an equilateral triangle?
Every equilateral triangle is equiangular, and every equiangular triangle is equilateral.
Is every isosceles triangle equiangular?
No but an equilateral triangle is equiangular
Is a equiangular triangle same as an equilateral?
Yes. If a triangle is equiangular, then it is also equilateral - and vice versa.
Are equilateral triangles equiangular?
Yes, all the angles of an equilateral triangle are always 60 degrees.
Triangle that is both equilateral and equiangular?
A triangle is equilateral if, and only if, it is equiangular. That is to say, the two statements are equivalent.
What is Triangle that is both equilateral and equiangular?
A triangle is equilateral if, and only if, it is equiangular. That is to say, the two statements are equivalent.
If a triangle is equilateral then it is?
equiangular.
What figures is not always equilateral square rhombus or rectangle?
A rectangle is not always equilateral, although it is always equiangular. A rhombus is not always equiangular, but is always equilateral. A square is both equilateral and equiangular.
