Prove that the sum of angles in a triangle is 180∘.
Let's assume that the sum of interior angles of this triangle is not 180 degrees. Now, we will draw a line segment PQ, parallel to the base BC such that sides AB and AC are transversals with respect to PQ and BC.
Angle PAB is equal to Angle ABC, and Angle QAC is equal to Angle ACB. This is because they are interior alternate angles to each other.
Angle PAB, Angle QAC and Angle BAC all lie on the same straight line PQ, and their sum is equal to the sum of interior angles of the triangle.
Now, let's remember our assumption from earlier. That, the sum of interior angles of a triangle is not 180 degrees.
Since we know that the sum of angles on ome side of a straight line is 180 degrees, we can say that our assumption was false.
Thus, we can say that the sum of interior angles in a triangle is the same as that on one side of a straight line; 180 degrees.
Let's assume that the sum of interior angles of this triangle is not 180 degrees. Now, we will draw a line segment PQ, parallel to the base BC such that sides AB and AC are transversals with respect to PQ and BC.
Angle PAB is equal to Angle ABC, and Angle QAC is equal to Angle ACB. This is because they are interior alternate angles to each other.
Angle PAB, Angle QAC and Angle BAC all lie on the same straight line PQ, and their sum is equal to the sum of interior angles of the triangle.
Now, let's remember our assumption from earlier. That, the sum of interior angles of a triangle is not 180 degrees.
Since we know that the sum of angles on ome side of a straight line is 180 degrees, we can say that our assumption was false.
Thus, we can say that the sum of interior angles in a triangle is the same as that on one side of a straight line; 180 degrees.
