Angle sum property:
The sum of the three angles in a triangle is equal to
Eg: If A, B and C are the angles of a triangle, then
Suppose a line XY is parallel to side BC. AB is a transversal that cuts line XY and AB, at A and B, respectively. As the alternate interior angles are equal, . Also, . form a linear pair, and their sum is .
Exterior angle property:
An exterior angle of a triangle is equal to the sum of its opposite interior angles.
Eg: In the figure here, ∠4 is called the exterior angle
to triangle ABC, and ∠4 = ∠1 + ∠2.
The sum of the lengths of any two sides of a triangle is greater than the third side.
In a right-angled triangle, the side opposite the right angle is called the hypotenuse, and the other two sides are called its legs.
In a right-angled triangle, the square of the hypotenuse is
equal to the sum of the squares of the other two legs.
a2 = b2 + c2
If the Pythagoras property holds, then the triangle must be right-angled. That is, if there is a triangle such that the sum of the squares on two of its sides is equal to the square of the third side, then it must be a right-angled triangle.