**Solutions for Class 7 Maths Chapter 6 The Triangle & Properties of Triangles**

In this article, we are going to explain **CBSE Class 7 Maths Triangle and Properties of Triangles. **A **triangle** is a simple closed curve made of three line segments. It has three vertices, three sides and three angles.

__Angle sum properties__

The sum of the three interior angles of a triangle is 180°. This property helps us solve a wide variety of problems based on Triangles.

e.g. If X, Y and Z are the angles of a triangle XYZ, then ∠X + ∠Y + ∠Z = 180°.

**Proof**:

Consider a triangle XYZ.

Let line AB be parallel to the side YZ at X.

XY is a transversal that cuts the line AB and XY, at X and Y, respectively.

The alternate interior angles are equal as ∠1 = ∠4 and ∠2 = ∠5.

∠4, ∠3 and ∠5 form linear angles, and the sum of three angles are equal to 180°.

⇒ ∠4 + ∠3 + ∠5 = 180°

⇒ ∠1 + ∠2 + ∠3 = 180°

Hence, the sum of the three interior angles of a triangle is 180°.

__Exterior angle property__

The sum of its opposite interior angles triangle is equal to an exterior angle.

e.g. If ∠4 is an exterior angle of ΔXYZ, ∠1 and ∠2 are the interior opposite angles, then ∠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, two sides are called its *legs.*

And the opposite side to the right angle is called the ** hypotenuse** .

__Pythagorean theorem__In a right-angled triangle, the is equal to the sum of the squares of the two sides (legs) is equal to the square of the hypotenuse .

** **If a and b are legs and c is the hypotenuse of a right angled triangle, then, c

^{2}= a

^{2}+ b

^{2}.

**If the sum of the squares on two sides of a triangle is equal to the square of the third side, then the triangle is a right-angled triangle.**

__Converse of Pythagorean theorem__

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