Maharashtra Board Class 6 Maths part 2 Chapter 15 Triangles and their Properties PDF Download

Triangles And Their Properties

Let's Discuss

In the figure alongside, some points and some line segments joining them have been drawn.

Which of these figures is a triangle?

Which figure is not a triangle? Why not?

Triangle ABC has three sides. Line segment AB is one side. Write the names of the other two sides.

Triangle ABC has three angles. Angle ABC is one of them. Write the names of the other angles.

Points A, B and C are called the vertices of the triangle.

Let's Learn

A triangle is a closed figure made by joining three non-collinear points by line segments.

The vertices, sides and angles of a triangle are called the parts of the triangle.

Teacher's Note

A triangle is like a three-sided shape. Think of a slice of pizza or a roof of a house. Both have three corners and three sides.

Exam Trick

Remember: A triangle has exactly THREE sides, THREE angles, and THREE vertices. If any of these numbers are wrong, it is not a triangle!

Points to Remember

A triangle is a closed figure with three sides.

The three corners are called vertices.

The three line segments are called sides.

The three angles are called angles of the triangle.

Types Of Triangles Based On Sides

Measure the sides of the following triangles in centimetres, using a divider and ruler.

Enter the lengths in the table below. What do you observe?

'Length of line segment AB' is written as l(AB).

In the table above, the lengths of all sides of triangle ABC are equal. Therefore, this triangle is an equilateral triangle.

'Lateral' refers to the sides of a figure.

A triangle with all three sides equal is called an equilateral triangle.

In triangle PQR, the length of the two sides PQ and PR are equal. Triangle PQR is called an isosceles triangle.

A triangle with two equal sides is called an isosceles triangle.

The lengths of the sides of triangle XYZ are all different. Such a triangle is called a scalene triangle.

A triangle with no two sides equal is called a scalene triangle.

Teacher's Note

Equilateral means all sides are equal. Like a square tile has four equal sides, an equilateral triangle has three equal sides. An isosceles triangle is like an ice cream cone shape where two sides are equal.

Exam Trick

Remember: Equilateral = all three sides equal. Isosceles = two sides equal. Scalene = no sides equal. Use the first letter to remember: E for equal (equilateral), I for identical two sides (isosceles), S for single (scalene).

Points to Remember

Equilateral triangle has all three sides equal in length.

Isosceles triangle has two sides equal in length.

Scalene triangle has all three sides different in length.

Types Of Triangles Based On Angles

Measure all the angles of the triangles given below. Enter them in the following table.

In the figures above, triangle DEF is an acute angled triangle.

A triangle with all three acute angles is called an acute angled triangle.

Triangle PQR is a right angled triangle.

A triangle with one right angle is a right angled triangle.

Triangle LMN is an obtuse angled triangle.

A triangle with one obtuse angle is called an obtuse angled triangle.

Teacher's Note

An acute angle is small, less than 90 degrees. A right angle is exactly 90 degrees like a corner of your book. An obtuse angle is bigger than 90 degrees like when you open a door wide. Every triangle has one type based on its angles.

Exam Trick

Remember: Acute angled = all angles small (less than 90°). Right angled = one 90° angle (like a square corner). Obtuse angled = one big angle (more than 90°). The set square in your geometry box is a right angled triangle.

Points to Remember

Acute angled triangle has all three angles less than 90 degrees.

Right angled triangle has one angle exactly 90 degrees.

Obtuse angled triangle has one angle more than 90 degrees.

Properties Of A Triangle

Activity: Take a triangular piece of paper. Choose three different colours or signs to mark the three corners of the triangle on both sides of the paper. Fold the paper at the midpoints of two sides as shown in the pictures.

m∠A + m∠B + m∠C = 180°

Activity: Take a triangular piece of paper and make three different types of marks near the three angles. Take a point approximately at the centre of the triangle. From this point, draw three lines that meet the three sides. Cut the paper along those lines. Place the three angles side by side as shown.

See how the three angles of a triangle together form a straight angle, or, an angle that measures 180°.

The sum of the measures of the three angles of a triangle is 180°.

Activity: Draw any triangle on a paper. Name its vertices A, B, C. Measure the lengths of its three sides using a divider and scale and enter them in the table.

The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

Teacher's Note

All three angles of any triangle always add up to 180 degrees. This is like a straight line. Also, if you add any two sides, the answer is always bigger than the third side. This rule helps us check if we can make a triangle from three sticks.

Exam Trick

Remember: Angle sum = 180°. Triangle inequality = sum of two sides is greater than the third side. In exams, always check if two sides add up to more than the third side before saying a triangle can be made.

Points to Remember

The sum of all three angles in any triangle is always 180 degrees.

The sum of any two sides must be greater than the third side.

You cannot make a triangle if the sum of two sides is not greater than the third side.

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