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Chapter 3

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Chapter 3

Perpendicular and Parallel Lines

- Two lines are PARALLEL LINESif they are coplanar and they do not intersect.
- Two lines are SKEW LINES if they are not coplanar and they do not intersect.
- Two planes that do not intersect are called PARALLEL PLANES.

- If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.

P

- A TRANSVERSAL is a line that intersects two or more coplanar lines at different points.

- Two angles are corresponding angles if they occupy corresponding positions.

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- Two angles are alternate interior angles if they lie between the two lines on opposite sides of the transversal.

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- Two angles are alternate exterior angles if they lie outside the two lines on opposite sides of the transversal.

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- Two angles are consecutive int. angles if they lie between the two lines on the same side of the transversal. (aka: same side interior angles)

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- UT and WT are: _________
- RS and VW are: ___________
- TW and WX are: ___________

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S

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- Name a line parallel to HJ.
- Name a line skew to GH.
- Name a line perpendicular to JH.

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- 6 and 10 are __________ angles.
- 12 and 6 are __________ angles.
- 7 and 9 are __________ angles.

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- If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.

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h

g h

- If two sides of two adjacent angles are perpendicular, then the angles are complementary.

- If two lines are perpendicular, then they intersect to form four right angles.

- Corresponding Angles Postulate
- If 2 parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

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- If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

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- If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.

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- If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

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- If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.

- Find m 1 and m 2.

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105

- Find m 1 and m 2.

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135

- Find x.

64

2x

- Find x.

(3x – 30)

3.4 is basically the converse of 3.3.

- If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.

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- If two parallel lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.

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- If two parallel lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel.

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- If two parallel lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.

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- If two lines are parallel to the same line, then they are parallel to each other.

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- In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

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- State which pair of lines are parallel and why.
- m A = m 6

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- m 6 = m 8

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- 1 = 90 , 5 = 90

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1 = 4

6 = 4

2 + 3 = 5

1 = 7

1 = 8

2 + 3 + 8 = 180

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- Given: AB II EF , AE II BF

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C

(2x-7)

(3x-34)

(4y+1)

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- Slope of a line:
- The equation of a line:
- Slope-intercept form: y = mx + b
- Point-slope form: y – y1 = m (x – x1)

- In a coordinate plane, two nonvertical lines are parallel iff they have the same slope. (Any two vertical lines are parallel.)
- In a coordinate plane, two nonvertical lines are perpendicular iff the product of their slopes is -1. (Vertical and horizontal lines are perpendicular.)

- Parallel lines have the same slopes.
- Perpendicular lines have slopes that are OPPOSITE RECIPROCALS. (Line 1 has a slope of -2. Line 2 is perpendicular to Line 1 and has a slope of ½ .

- Horizontal lines have a slope = 0 (zero)
- The equation of a horizontal line is y = b

- Vertical lines have undefined slope (und)
- The equation of a vertical line is x = a

- Write the equation of the line that goes through (1,1) with a slope of 2.

- Find the slope of the line between the points (0,6) and (5,2). Then write the equation of the line.

- Line 1 passes through (0,6) and (2,0).
- Line 2 passes through (-2,6) and (0,1).
- Line 3 passes through (-6,5) and (-4,0)

- Line 1 passes through (4,2) and (1,-4).
- Line 2 passes through (-1,2) and (5,-1).

- Write the equation of the line which passes through point (4,9) and has a slope of -2.

- Write the equation of the line parallel to the line y = -2/5 x + 3 and passing through the point (-5,0).

- Write the equation of the line parallel to the line 3x + 2y = 4 and passing through the point (-4, 5).

- Write the equation of the line parallel to the x-axis and passing through the point (3,-6).

- Write the equation of the line parallel to the y-axis and passing through the point (4,8).

- Line p1 passes through (0,-3) & (1,-2). Line p2 passes through (5,4) & (-4,-4). Line p3 passes through (-6,-1) & (3,7). Find the slope of each line. Which lines are parallel?

- Find the slope of the line passing through the given points.

- Determine if the two lines are parallel.

- What is the slope of the line?

- Find the slope of the line that passes through the given points.

- Determine if the two lines are parallel.

- With the given slopes, are the lines perpendicular?
- m1 = 2 ; m2 = - ½
- m1 = -1 ; m2 = 1
- m1 = 5/7 ; m2 = - 7/5

- Find the slopes of the two lines. Determine if they are perpendicular.

- Line 1: y = 3x ; Line 2: y = (-1/3)x – 2
- Line 1: y = (1/3)x – 10 ; Line 2: y = 3x

- Line 1: 3y + 2x = -36 ; Line 2: 4y – 3x = 16
- Line 1: 3y – 4x = 3 ; Line 2: 4y + 3x = -12

- Write the equation of the line perpendicular to the line y = (-3/4)x + 6 that goes through the point (8,0)

- Write the equation of the line that goes through point (-3,-4) and that is perpendicular to y = 3x + 5.

y = -2x – 1

y = -2x – 3

y = 4x + 10

y = -2x + 5