Prove that the sum of the measures of the interior angles of a triangle is 180°.
We will use the concept of angles on straight lines to prove that the sum of the measures of the interior angles of a triangle is 180°.
Answer: The sum of the measures of the interior angles of a triangle is 180°can be proved using the concept of angles on straight lines.
Let us see how we will use the concept of angles on straight lines to prove that the sum of the measures of the interior angles of a triangle is 180°.
Explanation:
Let us consider a triangle ABC as shown in the figure and construct a straight line PQ passing through A and parallel to BC.
Now, since PQ is parallel to BC.
∠PAB = ∠B and ∠QAC = ∠ C [alternate interior angles]
Now since ∠PAB + ∠A + ∠QAC = 180° [angles on a straight line]
Hence, ∠A + ∠B + ∠C = 180°