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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

1. Pairs of Lines and Angles

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Exercise 5 Page 501

Remember, the line must contain point B.

BF

Practice makes perfect

We are given a diagram. We want to find the line(s) that contain point B and are skew to CD. To do so we will first extend the line.

We will recall the definition of skew lines.

Skew Lines
Lines in three dimensions that don't intersect and are non-parallel.

By the definition notice that the lines that are skew to CD must meet two criteria.

They cannot be coplanar with CD.
They cannot intersect CD.

Due to these restrictions, the skew line(s) cannot run along the edges of plane ABCD. Therefore, the skew lines to CD are AE, BF, FG, and EH. Among these lines BF contains point B, so the line that fits the given description is BF.

Consequently, we can conclude that there is only one line that contain point B and is skew to CD and this line is BF.

Subchapter links

Communicate Your Answer p.497

Monitoring Progress p.498-500

Exercises p.501-502