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01.12.2020 •
Mathematics
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
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Ответ:
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°.
Ответ: