NCERT Class 9 Maths Lab Manual – Verify that the Sum of the Angles of a Triangle is 180°
To verify that the sum of the angles of a triangle is 180°.
- Cardboard sheet
- White chart paper
- Geometry box
- Drawing sheet
- Tracing paper
- Knowledge of straight angle
- Concept of triangle and its properties
- For straight line angle refer to Activity 11.
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.
- 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.
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°
Measure of ∠A = ………… ,
Measure of ∠B = ………… ,
Measure of ∠C = ………… ,
Hence, sum (∠A + ∠B + ∠C) = ………… .
The sum of angles of a triangle is 180°, have been verified.
This result can be used in many geometrical problems such as to find the sum of angles of a quadrilateral, pentagon and hexagon etc.
What is the angle sum property of a triangle?
The sum of angles of a triangle is 180°.
In a triangle, if the sum of two angles is 60°, then what will be the measure of third angle?
In a triangle, if one of the angles is 80°, then what will be the sum of other angles?
180° – 80° = 100°, Le. the sum of other angles = 100°.
If a triangle has all three angles are equal in measure, then what will the measure of each angle mark?
180°/30° = 60°.
What do we mean by scalene triangle?
A triangle whose all the three sides are unequal, is called scalene triangle.
Find the sum of the angles of pentagon and hexagon.