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Lesson 2-3: Pairs of Lines

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1 Lesson 2-3: Pairs of Lines

2 Lesson 2-3: Pairs of Lines
Parallel Lines Parallel lines are coplanar lines that do not intersect. Arrows are used to indicate lines are parallel. The symbol used for parallel lines is ||. In the above figure, the arrows show that line AB is parallel to line CD. With symbols we denote, Lesson 2-3: Pairs of Lines

3 Lesson 2-3: Pairs of Lines
PERPENDICULAR LINES Perpendicular lines are lines that intersect to form a right angle. The symbol used for perpendicular lines is  . 4 right angles are formed. m n In this figure line m is perpendicular to line n. With symbols we denote, m  n Lesson 2-3: Pairs of Lines

4 Skew Lines and Parallel Planes
Two lines are skew if they do not intersect and are not in the same plane (not coplanar). Ex: All planes are either parallel or intersecting. Parallel planes are two planes that do not intersect. Ex: Plane ABC and Plane EFG Lesson 2-3: Pairs of Lines

5 Lesson 2-3: Pairs of Lines
Examples: Name all segments that are parallel to Name all segments that intersect Name all segments that are skew to Name all planes that are parallel to plane ABC. Answers: Segments BC, FG, & EH. Segments DH, DC, AE & AB. Segments CG, BF, FE, & GH. Plane FGH. Lesson 2-3: Pairs of Lines

6 Lesson 2-4: Angles and Parallel Lines
Transversal Definition: A line that intersects two or more lines in a plane at different points is called a transversal. When a transversal t intersects line n and m, eight angles of the following types are formed: Exterior angles Interior angles Consecutive interior angles Alternative exterior angles Alternative interior angles Corresponding angles t m n Lesson 2-4: Angles and Parallel Lines

7 Vertical Angles & Linear Pair
Two angles that are opposite angles. Vertical angles are congruent.  1   4,  2   3,  5   8,  6   7 Supplementary angles that form a line (sum = 180) 1 & 2 , 2 & 4 , 4 &3, 3 & 1, 5 & 6, 6 & 8, 8 & 7, 7 & 5 1 2 3 4 5 6 7 8 Lesson 2-4: Angles and Parallel Lines

8 Corresponding Angles & Consecutive Angles
Corresponding Angles: Two angles that occupy corresponding positions.  2   6,  1   5,  3   7,  4   8 1 2 3 4 5 6 7 8 Lesson 2-4: Angles and Parallel Lines

9 Lesson 2-4: Angles and Parallel Lines
Consecutive Angles Consecutive Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal. Consecutive Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal. m3 +m5 = 180º, m4 +m6 = 180º 1 2 m1 +m7 = 180º, m2 +m8 = 180º 3 4 5 6 7 8 Lesson 2-4: Angles and Parallel Lines

10 Lesson 2-4: Angles and Parallel Lines
Alternate Angles Alternate Interior Angles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair). Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal.  3   6,  4   5  2   7,  1   8 1 2 3 4 5 6 7 8 Lesson 2-4: Angles and Parallel Lines

11 Lesson 2-3: Pairs of Lines

12 Slope of Parallel and Perpendicular lines
The slope of the non vertical line through the points and is m = The slope of a vertical line is not defined. The slope of a horizontal line is zero. Two lines are parallel if and only if they have equal slopes. Two lines are perpendicular if and only if the product of their slopes is -1 (reciprocals and opposite signs). Lesson 2-3: Pairs of Lines

13 Lesson 2-3: Pairs of Lines
Examples: Find the slope of the line through the given points. (-4, 7) and (3, 7) (3, -1) and (3, 2) (1, -4) and (2, 5) (-2, 5) and (1, -1) Lesson 2-3: Pairs of Lines

14 Lesson 2-3: Pairs of Lines
Examples Any line parallel to a line with slope has slope _____. Any line perpendicular to a line with slope has slope ___. Any line parallel to a line with slope 0 has slope _____. Any line perpendicular to a line with undefined slope has slope. Any line parallel to a line with slope 2 has slope _____. Zero Slope 2 Lesson 2-3: Pairs of Lines


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