Question

In the diagram provided, line I is parallel to line m. Select which of the following statements could be used to prove that

Answer 1

Answer: There is only one answer and it is choice B

Angle 1 and angle 4 are alternate interior angles

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Explanation

• A. This is false because it should be angle 4 + angle 5 = 180 without the angle 6. Adding on angle 6 results in some angle larger than 180. Note how angle 5 = (angle 3)+(angle 6).
• B. This is true and useful to showing that the three angles of a triangle add to 180 degrees. This is because you'll use the fact that angles 4, 5 and 6 combine to 180 degrees.
• C. While this is a true statement by the exterior angle theorem, it is not useful to the proof. It is better to state that angle 2 and angle 6 are congruent because they are alternate interior angles.
• D. Like choice C, it is true but not useful. It's better to say that angle 1 is congruent to angle 4. See choice B above.

Note how it's not enough for a statement to be true. It also needs to be relevant or useful to the context at hand. A more simpler example of this could be stating that x+x = 2x.