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: It is true that the sum of the measures of the interior angles of a triangle is 180°.
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°