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, c2 = a2 + b2.
Converse of Pythagorean theorem
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.
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