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Splash Screen. 1. In the figure, m 4 = 146. Find the measure of 2. 2. In the figure, m 4 = 146. Find the measure of 7. 3. In the figure, m 4 = 146. Find the measure of 10. 4. In the figure, m 4 = 146. Find the measure of 11. 5. Find m 11 + m 6. 5-Minute Check 1. - PowerPoint PPT PresentationTRANSCRIPT
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Over Lesson 3–2
1. In the figure, m4 = 146. Find the measure of 2.
4. In the figure, m4 = 146. Find the measure of 11.
2. In the figure, m4 = 146. Find the measure of 7.
3. In the figure, m4 = 146. Find the measure of 10.
5. Find m11 + m6.
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You used the properties of parallel lines to determine congruent angles.
• Find slopes of lines.
• Use slope to identify parallel and perpendicular lines.
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• slope
• rate of change
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Find the Slope of a Line
A. Find the slope of the line.
Substitute (–3, 7) for (x1, y1) and (–1, –1) for (x2, y2).
Answer: –4
Slope formula
Substitution
Simplify.
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Find the Slope of a Line
B. Find the slope of the line.
Substitute (0, 4) for (x1, y1) and
(0, –3) for (x2, y2).
Answer: The slope is undefined.
Slope formula
Substitution
Simplify.
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Find the Slope of a Line
C. Find the slope of the line.
Answer:
Slope formula
Substitution
Simplify.
Substitute (–2, –5) for (x1, y1) and (6, 2) for (x2, y2).
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Find the Slope of a Line
D. Find the slope of the line.
Answer: 0
Slope formula
Substitution
Simplify.
Substitute (–2, –1) for (x1, y1) and (6, –1) for (x2, y2).
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A.
B.
C.
D.
A. Find the slope of the line.
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A. 0
B. undefined
C. 7
D.
B. Find the slope of the line.
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A. 0
B. undefined
C. 3
D.
D. Find the slope of the line.
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Determine Line Relationships
Step 1 Find the slopes of and .
Determine whether and are parallel, perpendicular, or neither for F(1, –3), G(–2, –1), H(5, 0), and J(6, 3). Graph each line to verify your answer.
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Determine Line Relationships
Step 2 Determine the relationship, if any, between the
lines.The slopes are not the same, so and are not parallel. The product of the slopes is
So, and are not
perpendicular.
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Determine Line Relationships
Answer: The lines are neither parallel nor perpendicular.
Check When graphed, you can see that the lines are
not parallel and do not intersect in right angles.
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A. parallel
B. perpendicular
C. neither
Determine whether AB and CD are parallel, perpendicular, or neither for A(–2, –1), B(4, 5), C(6, 1), and D(9, –2)
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Use Slope to Graph a Line
First, find the slope of .
Slope formula
Substitution
Simplify.
Graph the line that contains Q(5, 1) and is parallel to MN with M(–2, 4) and N(2, 1).
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Use Slope to Graph a Line
The slope of the line parallel to through Q(5, 1) is .
The slopes of two parallel lines are the same.
Graph the line.
Draw .
Start at (5, 1). Move up 3 units and then move left 4 units.
Label the point R.
Answer:
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Graph the line that contains R(2, –1) and is parallelto OP with O(1, 6) and P(–3, 1).
A. B.
C. D. none of these
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