7-3 Parallel and Perpendicular Lines
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1 Learn to identify parallel, perpendicular, and skew lines, and angles formed by a transversal.
2 7-3 Parallel Insert Lesson and Perpendicular Title Here Lines Vocabulary perpendicular lines parallel lines skew lines vertical angles transversal
3 When lines, segments, or rays intersect, they form angles. If the angles formed by two intersecting lines are equal to 90, the lines are perpendicular lines. Some lines in the same plane do not intersect at all. These lines are parallel lines. Segments and rays that are part of parallel lines are also parallel. Skew lines do not intersect, and yet they are also not parallel. They lie in different planes.
4 Reading Math The symbol means is parallel to. The symbol means is perpendicular to.
5 Additional Example 1A: Identifying Parallel, Perpendicular, and Skew Lines Tell whether the lines appear parallel, perpendicular, or skew. X Y W U Z V A. UV and YV UV YV The lines appear to intersect to form right angles.
6 Additional Example 1B: Identifying Parallel, Perpendicular, and Skew Lines Tell whether the lines appear parallel, perpendicular, or skew. X Y W U Z V B. XU and WZ XU and WZ are skew. The lines are in different planes and do not intersect.
7 Additional Example 1C: Identifying Parallel, Perpendicular, and Skew Lines Tell whether the lines appear parallel, perpendicular, or skew. X Y W U Z V C. XY and WZ XY WZ The lines are in the same plane and do not intersect.
8 Try This: Example 1A Tell whether the lines appear parallel, perpendicular, or skew. X Y W U Z V A. WX and XU WX XU The lines appear to intersect to form right angles.
9 Try This: Example 1B Tell whether the lines appear parallel, perpendicular, or skew. X Y U V W Z B. WX and UV WX and UV are skew The lines are in different planes and do not intersect.
10 Try This: Example 1C Tell whether the lines appear parallel, perpendicular, or skew. X Y W U Z V C. WX and ZY WX ZY The lines are in the same plane and do not intersect.
11 Vertical angles are the opposite angles formed by two intersecting lines. When two lines intersect, two pairs of vertical angles are formed. Vertical angles have the same measure, so they are congruent.
12 A transversal is a line that intersects two or more lines. Eight angles are formed when a transversal intersects two lines. When those two lines are parallel, all of the acute angles formed are congruent, and all of the obtuse angles formed are congruent. These obtuse and acute angles are supplementary
13 Reading Math Angles with the same number of tick marks are congruent. The tick marks are placed in the arcs drawn inside the angles.
14 Additional Example 2A: Using Angle Relationships to Find Angle Measures Line n line p. Find the measure of the angle. A. 2 2 and the 130 angle are vertical angles. Since vertical angles are congruent, m 2 = 130.
15 Additional Example 2B: Using Angle Relationships to Find Angle Measures Line n line p. Find the measure of the angle. B. 3 3 and the 50 angle are acute angles. Since all of the acute angles in the figure are congruent, m 3 = 50.
16 Additional Example 2C: Using Angle Relationships to Find Angle Measures Line n line p. Find the measure of the angle. C. 4 4 is an obtuse angle. Since all of the obtuse angles in the figure are congruent, m 4 = 130.
17 Try This: Example 2A Line n line p. Find the measure of the angle A. 3 3 and the 45 angle are vertical angles. Since vertical angles are congruent, m 3 = 45. n p
18 Try This: Example 2B Line n line p. Find the measure of the angle B. 6 6 and the 135 angle are obtuse angles. Since vertical angles are congruent, m 6 = 135. n p
19 Try This: Example 2C Line n line p. Find the measure of the angle C. 4 n 4 is an obtuse angle. m = m 4 = 135 p In the figure, the acute and obtuse angles are supplementary. Subtract 45 to isolate m 4.
20 7-3 Parallel Insert Lesson and Perpendicular Title Here Lines Lesson Quiz Tell whether the lines appear parallel, perpendicular, or skew. 1. AB and CD 2. EF and FH 3. AB and CG parallel perpendicular skew D 4. How are railroad tracks and two parallel lines alike, and how are they different? Both are always the same distance apart, but railroad tracks are not always straight.
21 Homework 7-3 Worksheet
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