Question

How could you use coordinate geometry to prove that segment BC is congruent to segment AD?

1.) Prove the slopes are the same.

2.) Prove the slopes are opposite reciprocals.

3.) Prove the lengths are the same.

4.) Prove the midpoints are the same.

Answer 1

To prove that segment BC is congruent to segment AD using coordinate geometry, you can follow these steps: 1) Prove the slopes are the same. 2) Prove the slopes are opposite reciprocals. 3) Prove the lengths are the same. 4) Prove the midpoints are the same.

Step-by-step explanation:

To prove that segment BC is congruent to segment AD using coordinate geometry, we can follow these steps:

1. Prove the slopes are the same: Find the slopes of lines BC and AD by using the formula (change in y)/(change in x). If the slopes are equal, it implies that the lines are parallel.
2. Prove the slopes are opposite reciprocals: If the slopes of lines BC and AD are opposite reciprocals of each other, it implies that the lines are perpendicular.
3. Prove the lengths are the same: Calculate the distance between points B and C and compare it to the distance between points A and D. If the distances are equal, it implies that the segments are congruent.
4. Prove the midpoints are the same: Calculate the coordinates of the midpoint of segment BC and compare it to the coordinates of the midpoint of segment AD. If the midpoints are the same, it implies that the segments are congruent.