What is the Relationship between DE and BC?

Understanding Parallel Lines

In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. When two lines in a plane intersect each other at a right angle, they are said to be perpendicular. The general equation of a straight line is y = mx + b, where m is the slope of the line and b is the y-intercept.

Understanding the Given Figure

The given figure shows two lines DE and BC which intersect each other at point A. The figure also shows that line DE is parallel to line BC. The lines DE and BC are parallel because they have the same slope and the same y-intercept.

Proving That DE is Parallel to BC

To prove that DE is parallel to BC, we first need to calculate the slopes of the two lines. The slope of the line DE is m1 = (A.y – B.y)/(A.x – B.x) and the slope of the line BC is m2 = (A.y – C.y)/(A.x – C.x). Then, if m1 = m2, then the two lines are parallel.

Conclusion

From the given figure, we can conclude that line DE is parallel to line BC. This can be proven by calculating the slopes of the two lines and verifying that they are equal.

References

1. Khan Academy. (n.d.). Parallel lines and transversals. Retrieved from https://www.khanacademy.org/math/basic-geo/basic-geo-lines/parallel-lines-and-transversals/v/parallel-lines-and-transversal-2