Question

Given that p || q, what are the reasons that each statement is true?

Answer 1

1. Given.

2. Vertical angles are congruent.

3. If two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.

4. Vertical angles are congruent.

5. Substitution.

Step-by-step explanation: Edge Sample Response!

Answer 2

See answers below

Explanation:

1) This is the given premise "line p is parallel to line q"

2) Angles 1 and 2 are equal (congruent) because they are vertical opposite angles.

3) Angles 2 and 3 are equal (congruent) because they are alternate angles.

4) Angles 3 and 4 are equal (congruent) because they are vertical opposite angles.

5) Angles 1 and 4 are equal (congruent) because: a) angle 1 is equal to angle 2 being vertical opposite, b) angle 2 is equal to angle 4 because they are corresponding angles, therefore c) due to transitive property, angle 1 will equal angle 4.