RD Sharma Class 7 Maths Solutions Chapter 15 - Properties of Triangles

In this Chapter 15 - Properties of Triangles, several exercise questions with solutions for RD Sharma Class 7 Maths are given to help the students and understand the concepts better. 

We have provided step by step solutions for all exercise questions given in the PDF of Class 7 RD Sharma Chapter 15 - Properties of Triangles. All the Exercise questions with solutions in Chapter 15 - Properties of Triangles are given below:

Exercise 15.1

Exercise 15.2

Exercise 15.3

Exercise 15.4

Exercise 15.5

From each vertex, one Altitude can be produced. A Triangle has 3 Altitudes.These are some of the essential concepts that are explained in this Chapter:

• Medians of a Triangle

• Altitudes of a Triangle

• Property of Exterior Angle of a Triangle 

• Angle Sum Property of a Triangle

• Two Special Triangles: Equilateral and Isosceles

• The Sum of Lengths of Two Sides of A Triangle

• Right-Angled Triangles and Pythagoras Property

Medians of a Triangle

Median is a line segment that connects a vertex of a Triangle to the midpoint of the opposite side of the Triangle is called the Median. A Triangle has 3 Medians.

Altitudes of a Triangle

A perpendicular line segment that has one endpoint at a vertex or tip of the Triangle and the other on the line containing the opposite side is called the Altitude

Exterior Angle of a Triangle

When a side of a Triangle is made, an exterior angle of a Triangle is created. There are two ways of forming an exterior angle at each vertex. The sum of its interior opposite angles is equal to the exterior angle of a Triangle. The above relation is called the exterior angle property of a Triangle.

Angle Sum Property of a Triangle

The angle sum property of a Triangle states that The total sum of the three angles of a Triangle is equal to 180°.

Two Special Triangles: Equilateral and Isosceles

An equilateral is a Triangle in which all three sides are of equal lengths.

Thus, in an equilateral Triangle:

1. all sides have the same length.

2. each angle has a measure of 60°.

An isosceles Triangle is a Triangle in which two sides are of equal lengths.

Thus, in an isosceles Triangle:

1. two sides have the same length.

2. the base angles opposite to the equal sides are identical.

A base is the non-equal side of an isosceles Triangle.

Sum of the Lengths of Two Sides of A Triangle

Some characteristics of the lengths of sides of a Triangle:

• The length of the third side will always be lesser than the sum of the lengths of any two sides of a Triangle.

• The difference between the lengths of any two sides of the Triangle will always be smaller than the length of the third side.

This property is beneficial to know if it is feasible to draw a Triangle when the three sides of a Triangles’ length are given.

Right-Angled Triangles and Pythagoras Property

Pythagoras, a Greek Philosopher, discovered a very important property of right-angled Triangles.

The property is, therefore, named after him. 

We will now explain the Pythagoras property.

In right-angled Triangles, the sides have some specific names. 

• The side which is on the opposite of  the right angle is called its hypotenuse. 

• The remaining two sides are the legs of the right-angled Triangle.

The Pythagoras theorem may be stated ass:

a2= b2+ c2

Thus, the square on the hypotenuse = sum of the squares of the other two sides. 

If a Triangle is not right-angled, this property does not apply. This is helpful to determine if a Triangle is right-angled or not.