Question

Complete the proof to show that lines ac and bd which intersect at point b form a linear pair. Select the correct answer from each drop-down menu.

1) definition of linear pair
2) definition of a straight angle
3) angle addition postulate

Answer 1

To show lines ac and bd form a linear pair at their intersection point b, use the definition of a linear pair, definition of a straight angle, and the angle addition postulate to demonstrate the angles are supplementary.

Step-by-step explanation:

To complete the proof to show that lines ac and bd form a linear pair when they intersect at point b, we can follow these steps:

1. Invoke the definition of linear pair, which is a pair of adjacent, supplementary angles created when two lines intersect.
2. Use the definition of a straight angle to establish that a straight angle measures 180 degrees, which is relevant because each angle of a linear pair shares a common side and together they form a straight line.
3. Apply the angle addition postulate to add the two adjacent angles of the linear pair, demonstrating that their measures add up to 180 degrees, confirming that they are supplementary.

By following these logical steps and principles, we complete the proof that lines ac and bd intersecting at point b indeed form a linear pair.