Question

In the proof, what is the justification for the statement that segment CD intersects segment AB and creates angles 1, 2, 3, and 4?

1) Given
2) Transitive property
3) Subtraction property
4) Definition of supplementary angles
5) Intersecting lines postulate
6) Same-side interior angles theorem
7) Vertical angles theorem

Answer 1

The statement that segment CD intersects segment AB creating angles is justified by the Intersecting Lines Postulate and the Vertical Angles Theorem. This postulate states that if two lines intersect, then the angles formed at the intersection are congruent. In this case, segment CD intersects segment AB, creating angles 1, 2, 3, and 4. Therefore, the angles formed are congruent.

Step-by-step explanation:

The justification for the statement that segment CD intersects segment AB creating angles 1, 2, 3, and 4 is the Intersecting Lines Postulate. This postulate states that when two lines intersect, they form two pairs of opposite angles, also known as vertical angles, which are equal in measure. For the angles created by the intersection, we use the Vertical Angles Theorem to establish that the angles opposite each other are equal, meaning angle 1 is equal to angle 3, and angle 2 is equal to angle 4.