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Properties of Triangles

# Properties of Triangles

The sum of the three angles in a triangle

Lesson Demo

#### 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.

#### Pythagorean theorem:

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

#### Converse:

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.