John writes the proof below to show that the sum of the angles in a triangle is equal to 180°. Which of these reasons would John NOT use in his proof? A. The sum of the angles on one side of a straight line is 180°. B. If a statement about a is true and a=b, the statement formed by replacing a with b is also true. C. When two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent. D. When two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent. G-CO.10 2. In triangle ABC, ∠ = ∠ = . Which of these can be proved using the triangle s

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°.

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