Exercise 13 Page 537

Practice makes perfect

a Skew lines are lines that are neither parallel, coplanar or intersecting. We have a couple of such lines to choose from. For example, AB and all other lines. Therefore, an example for skew lines are

AB and GH Let's mark these in our figure.

b Perpendicular lines intersect to create a right angle. Again, we have a few lines we can choose from. For example

EF and IJ Let's mark these in our figure.

c Parallel lines run in the same direction. According to the Lines Perpendicular to a Transversal Theorem, we know that if two lines are perpendicular to the same line, then they are parallel to each other. From the figure we know that

EF ⊥ IJ and CD ⊥ IJ, Therefore EF and CD are parallel, Let's mark these in our figure.

d When a transversal intersects two or more coplanar lines, there are a few angles created. Corresponding angles refers to a pair of such angles that have corresponding positions around the transversal. We have already established that

CD ∥ EF. The line KL is a transversal to these lines lines making an example of corresponding angles are ∠ 1 and ∠ 3. Additionally, corresponding angles are congruent if the lines being cut are parallel, so ∠ 1 ≅ ∠ 3.

e Alternate interior angles are angles that are between the parallel lines and on opposite sides of the transversal. Since we know that

CD ∥ EF. we know that the alternate interior angles we find are congruent. A pair of such angles are ∠ 2 and ∠ 3.

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Exercise 13 Page 537

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