CBSE Class 9 Answered

Stat: Sum of the angle of a triangle is 180º.

Given: A triangle ABC in which the angles are a degree, b degree and c degree.

Construction Draw the line PAQ parallel to BC. Take the replica of ÐABC and put it in ÐPAB and ÐACB in ÐQAC

Proof: Now angle PAB= b degree and angle QAC= c degree since they are the pairs of alternate interior angles.

ÐPAB = b º [ Alternate interior angle]

ÐQAC = c º [ Alternate interior angle]

Now Angle PAB plus angle BAC plus angle QAC is equal to 180 degree

ÐPAB+ÐBAC+ÐQAC= 180º º [ Angle sum of straight line]

b º+ c º+ a º = 180º

Hence the angle sum of triangle is 180 º

Hence we have proved the sum of angles of a triangle to be 180 degree.