Angle sum property

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

In our previous classes, we have found the sum of three angles of a triangle. An activity is suggested here to find the sum of three angles of a triangle.

Activity

Draw a scalene triangle, an acute angled triangle, an obtuse angled triangle, an equilateral triangle and a right angled triangle. Measure the angles in all the figure.

Enter the measure in the table given. What do you observe? What do you conclude with respect to the sum of the magnitudes of all angles? What generalisation can you arrive at?

From the suggested activity you will find that the sum of three angles of a triangle is always equal to 180^o or two right angles. Let us now prove the same through logical deduction.