Exercise 24 Page 130

Practice makes perfect

a Let's extend the line that passes through points N and Q, NQ.

From the figure, we can see that NQ is a vertical line along one of the sides of the cube. Any line parallel to this line must also be vertical. We can find these lines along the remaining edges of the cube.

There are three parallel lines: RK, PM, and SL.

b Let's extend all of the lines that intersect NQ. Notice that each one will pass through either N or Q.

There are four lines that intersect NQ: KN, PQ, RQ, and MN.

c Lines that are skew to NQ are neither coplanar with NQ, nor do they intersect NQ. Examining the figure, we can determine that NQ is a part of two separate planes, NQR and NQP.

By the definition of skew, we can rule out any line that runs along either of these planes. PQ * MN * PM * KN * RQ * KR * This leaves five potential skew lines left. Let's mark these on the diagram.

Therefore, the lines that are skew to NQ are: ML, PS, RS, KL, and LS.

d If you were asked to name a street that is parallel to your own street, you wouldn't name your own street. The same logic applies here. We do not mention NQ as being parallel with, intersecting, or skew with itself.

Subchapter links

Communicate Your Answer p.125

Monitoring Progress p.126-128

Exercises p.129-130

Exercise 24 Page 130

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