**NCERT Class 9 Maths Lab Manual – Verify that the Sum of the Angles of a Triangle is 180°**

**OBJECTIVE**

To verify that the sum of the angles of a triangle is 180°.

**Materials Required**

- Cardboard sheet
- White chart paper
- Geometry box
- Scissors
- Adhesive
- Drawing sheet
- Tracing paper

**Prerequisite Knowledge**

- Knowledge of straight angle
- Concept of triangle and its properties

**Theory**

- For straight line angle refer to Activity 11.
**Triangle**

A plane figure closed by three intersecting lines is called a triangle, here Tri’ means ‘three’. A triangle has three sides, three angles and three vertices and it is denoted by the symbol ‘Δ’. A ΔABC is shown in Fig. 12.1.

**Some basic properties of triangles are given below :**

- The sum of all the angles of a triangle is always 180°.
- Angles opposite to equal sides of a triangle are equal.
- The sides opposite to equal angles in a triangle are equal.
- In a triangle, the angle opposite to longer side is larger and vice-versa.
- The sum of two sides of a triangle is greater than the third side.
- The exterior opposite angle in a triangle is equal to sum of opposite interior angles.

**Note:** The property (1) is called Angle Sum Property of triangle.

**Procedure**

- Take a cardboard of suitable size and by using adhesive, paste a white chart paper on it.
- Draw a ΔABC of suitable lengths on the drawing sheet and also mark all the angles as shown in Fig. 12.2.

- By using tracing paper, cut out the angles respectively equal to ∠A , ∠B and ∠C from a drawing sheet, (see Fig. 12.3).

- Now, draw a line on the cardboard and paste the cut outs of the angles (∠A, ∠B and ∠C) on the line at a point O as shown in Fig. 12.4.

**Demonstration**

When all the three cut outs of the angles A, B, C placed adjacent to each other at a point, then it forms a line forming a straight angle, i.e. 180°.

Flence, it is proved that the sum of the three angles of a triangle is 180°.

Therefore, ∠A + ∠B + ∠C =180°

**Observation**

Measure of ∠A = ………… ,

Measure of ∠B = ………… ,

Measure of ∠C = ………… ,

Hence, sum (∠A + ∠B + ∠C) = ………… .

**Result**

The sum of angles of a triangle is 180°, have been verified.

**Application**

This result can be used in many geometrical problems such as to find the sum of angles of a quadrilateral, pentagon and hexagon etc.

**Viva Voce**

**Question 1:**

What is the angle sum property of a triangle?

**Answer:**

The sum of angles of a triangle is 180°.

**Question 2:**

In a triangle, if the sum of two angles is 60°, then what will be the measure of third angle?

**Answer:**

180°-60° =120°.

**Question 3:**

In a triangle, if one of the angles is 80°, then what will be the sum of other angles?

**Answer:**

180° – 80° = 100°, Le. the sum of other angles = 100°.

**Question 4:**

If a triangle has all three angles are equal in measure, then what will the measure of each angle mark?

**Answer:
**180°/30° = 60°.

**Question 5:**

What do we mean by scalene triangle?

**Answer:**

A triangle whose all the three sides are unequal, is called scalene triangle.

**Suggested Activity**

Find the sum of the angles of pentagon and hexagon.

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