Lesson 3-5 Menu
14
1. Write an equation in point-slope form of a line having slope as ¾ and contains the point (5, –2). 2. Write an equation in point-slope form of a line having slope as 3 and contains the point (–2, 7). 3. Write an equation in slope-intercept form of a line having slope as –3 and contains the point (0, 2.5). 4. Write an equation in slope-intercept form of a line having slope as –½ and contains the point (4, –6). 5. Write an equation in slope-intercept form of a line passing through (1, 5) and (3, 11).
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Write an equation in point-slope form of a line having slope as ¾ and contains the point (5, –2). Write an equation in point-slope form of a line having slope as 3 and contains the point (–2, 7). - PowerPoint PPT Presentation
Transcript of Lesson 3-5 Menu
Lesson 3-5 Menu
1. Write an equation in point-slope form of a line having slope as ¾ and contains the point (5, –2).
2. Write an equation in point-slope form of a line having slope as 3 and contains the point (–2, 7).
3. Write an equation in slope-intercept form of a line having slope as –3 and contains the point (0, 2.5).
4. Write an equation in slope-intercept form of a line having slope as –½ and contains the point (4, –6).
5. Write an equation in slope-intercept form of a line passing through (1, 5) and (3, 11).
Lesson 3-5 Ideas/Vocabulary
• Recognize angle conditions that occur with parallel lines.
• Prove that two lines are parallel based on given angle relationships.
Since RQT and SQP are vertical angles, m SQP = 77.
Lesson 3-5 Example 1
Determine which lines, if any, are parallel.
Identify Parallel Lines
Since m UPQ + m SQP = 103 + 77 or 180, consecutive interior angles are supplementary. So, a || b.
Since m TQR + m VRQ = 77 + 100 or 177, consecutive interior angles are not supplementary. So, c is not parallel to a or b.Answer: a || b
Lesson 3-5 CYP 1
A. A
B. B
C. C
D. D
I only
II only
III only
I, II, and III
Determine which lines, if any are parallel.I. e || fII. e || gIII. f || g
ALGEBRA Find x and m ZYN so that || .
Lesson 3-5 Example 2
Solve Problems with Parallel Lines
Explore From the figure, you know that m WXP = 11x – 25 and m ZYN = 7x + 35. You also know that WXP and ZYN are alternate exterior angles.
Lesson 3-5 Example 2
Solve Problems with Parallel Lines
Plan For line PQ to be parallel to MN, the alternate exterior angles must be congruent. So, m WXP = m ZYN. Substitute the given angle measures into this equation and solve for x. Once you know the value of x, use substitution to find m ZYN.
Solvem WXP = m ZYN Alternate exterior angles
11x – 25 = 7x + 35 Substitution
4x – 25 = 35 Subtract 7x from each side.
4x = 60 Add 25 to each side.
x = 15 Divide each side by 4.
Lesson 3-5 Example 2
Solve Problems with Parallel Lines
Now use the value of x to find m ZYN.
Answer: x = 15, m ZYN = 140
m ZYN = 7x + 35 Original equation
= 7(15) + 35 x = 15
= 140 Simplify.
Examine Verify the angle measure by using the value of x to find m WXP. That is, 11x – 25 = 11(15) – 25 or 140. Since m WXP = m ZYN, m WXP m ZYN and || .
Lesson 3-5 CYP 2
A. A
B. B
C. C
D. D
ALGEBRA Find x so that || .
x = 60
x = 9
x = 12
x = 12
Lesson 3-5 Example 3
Prove Lines Parallel
Prove: r || s
Given: ℓ || m
Lesson 3-5 Example 3
Prove Lines Parallel
2. 2. Consecutive Interior Angle Theorem
5. 5. Substitution
6. 6. Definition of supplementary
angles7. 7. If consecutive interior angles
are supplementary, then lines are parallel.
1. 1. Given
Proof:Statements Reasons
4. 4. Definition of congruent angles
3. 3. Definition of supplementary
angles
Given x || y and , do you need to use theCorresponding Angles Postulate to prove a || b?
A. A
B. B
C. C
Lesson 3-5 CYP 3
yes
no
not enough informationto determine
Lesson 3-5 Example 4
Determine whether p || q.
Slope and Parallel Lines
slope of p:
slope of q:
Answer: Since the slopes are equal, p || q.
