Answer:
The correct option is;
D. When two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent
Step-by-step explanation:
In the proof to show that the sum of the angles in a triangle = 180°, we have;
For a triangle located between two parallel lines, such that the base of the triangle coincides with one of the parallel lines, we have;
The angle formed by one of the base angles and the adjacent side of the extension = 180° by the sum of angles on a straight line
From the attached diagram of a triangle between two parallel lines, we have;
∠e + ∠b = 180° by the sum of angles on a straight line postulate
∠e = ∠a + ∠d by alternate interior angles postulate
∠c = ∠d by alternate interior angles postulate
∴ ∠e = ∠a + ∠c by substitution property
∴ ∠e + ∠b = ∠a + ∠c + ∠b = 180° by substitution property
Therefore, the sum of the interior angles of a triangle, ∠a + ∠c + ∠b = 180°.
