The proof is pretty simple, but hard to see without the pictures. SO here is a link to the proof with some pics.
http://www.apronus.com/geometry/triangle.htm
The answer depends on your geometry: In Euclidean geometry, the angle sum is 180 degrees, in Hyperbolic geometry it is less than 180 degrees, and in Elliptical geometry it is greater than 180 degrees.
A triangle with no equal sides and no equal angles is called a scalene triangle. In contrast, a triangle with equal sides and equal angles is called an equilateral triangle. A triangle with two equal sides and two equal angles is an isosceles triangle.
An isosceles triangle has two equal angles.
An isosceles triangle has 2 equal sides and 2 equal angles.
A triangle that has three equal sides, and therefore three equal angles, is called an equilateral triangle.
It is an isosceles triangle.
Equilateral Triangles do not contain right angles, since all angles in this shape are equal and it is impossible to make a triangle that consists of three 90 degress angles. Isosceles and Scalene may contain a right angle.
A right triangle.
The Sum of the angles of a triangle drawn on a plain surface. is 180 degrees. However, the sum of the angles of a triangle drawn on a curved surface, such as a sphere ( the Earth) can be greater than 180 degrees.
It has 3 sides 2 of which are equal in length It has 3 angles 2 of which are the same size
A triangle with no equal sides and no equal angles is called a scalene triangle. In contrast, a triangle with equal sides and equal angles is called an equilateral triangle. A triangle with two equal sides and two equal angles is an isosceles triangle.
An EQUILATERAL Triangle. An ISOSCELES Triangle is two equal sides and two equal angles. A RIGHT-ANGLED Triangle has ONE right angle (90 degrees) A SCALENE Triangle has neither equal sides nor equal angles.
A right triangle can have 2 equal angles if they are each 45° (any other right triangle will have no equal angles)
An obtuse triangle can have no right angles, and has two equal angles.
Equilateral Triangle- 3 equal sides, 3 equal angles which are ALWAYS 60 degrees. Isosceles Triangle- Two equal sides, Two equal angles Scalene Triangle- No equal sides, and no equal angles
An isosceles triangle has 3 sides 2 of which are equal in length An isosceles triangle has 3 interior angles 2 of which are the same size
There is no such triangle because if it has two equal sides then it must have two equal angles such as an isosceles triangle
Corresponding angles must be equal; in this case, that would be angle f. To prove that the two triangles are equal, you would have to prove that at least another pair of angles is also equal, for example, angle b equal to angle d. Or prove some other facts, like the ratio between certain corresponding sides.