3-3 slopes of lines. ccss content standards g.gpe.5 prove the slope criteria for parallel and...
TRANSCRIPT
![Page 1: 3-3 Slopes of Lines. CCSS Content Standards G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems](https://reader036.vdocument.in/reader036/viewer/2022062422/56649ef05503460f94c001ff/html5/thumbnails/1.jpg)
3-3 Slopes of Lines
![Page 2: 3-3 Slopes of Lines. CCSS Content Standards G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems](https://reader036.vdocument.in/reader036/viewer/2022062422/56649ef05503460f94c001ff/html5/thumbnails/2.jpg)
CCSS
Content StandardsG.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).Mathematical Practices4 Model with mathematics.7 Look for and make use of structure.8 Look for and express regularity in repeated reasoning.
![Page 3: 3-3 Slopes of Lines. CCSS Content Standards G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems](https://reader036.vdocument.in/reader036/viewer/2022062422/56649ef05503460f94c001ff/html5/thumbnails/3.jpg)
Then/Now
You used the properties of parallel lines to determine congruent angles.
• Find slopes of lines.
• Use slope to identify parallel and perpendicular lines.
![Page 4: 3-3 Slopes of Lines. CCSS Content Standards G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems](https://reader036.vdocument.in/reader036/viewer/2022062422/56649ef05503460f94c001ff/html5/thumbnails/4.jpg)
Vocabulary
• slope
• rate of change
![Page 5: 3-3 Slopes of Lines. CCSS Content Standards G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems](https://reader036.vdocument.in/reader036/viewer/2022062422/56649ef05503460f94c001ff/html5/thumbnails/5.jpg)
Concept
![Page 6: 3-3 Slopes of Lines. CCSS Content Standards G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems](https://reader036.vdocument.in/reader036/viewer/2022062422/56649ef05503460f94c001ff/html5/thumbnails/6.jpg)
Concept
![Page 7: 3-3 Slopes of Lines. CCSS Content Standards G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems](https://reader036.vdocument.in/reader036/viewer/2022062422/56649ef05503460f94c001ff/html5/thumbnails/7.jpg)
A.
B.
C.
D.
Example 1aA. Find the slope of the line.
![Page 8: 3-3 Slopes of Lines. CCSS Content Standards G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems](https://reader036.vdocument.in/reader036/viewer/2022062422/56649ef05503460f94c001ff/html5/thumbnails/8.jpg)
A. 0
B. undefined
C. 7
D.
Example 1bB. Find the slope of the line.
![Page 9: 3-3 Slopes of Lines. CCSS Content Standards G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems](https://reader036.vdocument.in/reader036/viewer/2022062422/56649ef05503460f94c001ff/html5/thumbnails/9.jpg)
A.
B.
C. –2
D. 2
Example 1cC. Find the slope of the line.
![Page 10: 3-3 Slopes of Lines. CCSS Content Standards G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems](https://reader036.vdocument.in/reader036/viewer/2022062422/56649ef05503460f94c001ff/html5/thumbnails/10.jpg)
A. 0
B. undefined
C. 3
D.
Example 1dD. Find the slope of the line.
![Page 11: 3-3 Slopes of Lines. CCSS Content Standards G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems](https://reader036.vdocument.in/reader036/viewer/2022062422/56649ef05503460f94c001ff/html5/thumbnails/11.jpg)
Concept
![Page 12: 3-3 Slopes of Lines. CCSS Content Standards G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems](https://reader036.vdocument.in/reader036/viewer/2022062422/56649ef05503460f94c001ff/html5/thumbnails/12.jpg)
Example 3Determine 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.
![Page 13: 3-3 Slopes of Lines. CCSS Content Standards G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems](https://reader036.vdocument.in/reader036/viewer/2022062422/56649ef05503460f94c001ff/html5/thumbnails/13.jpg)
Example 3Determine Line Relationships
Step 2 Determine the relationship, if any, between thelines.
The slopes are not the same, so and are not parallel. The product of the slopes is
So, and are not
perpendicular.
![Page 14: 3-3 Slopes of Lines. CCSS Content Standards G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems](https://reader036.vdocument.in/reader036/viewer/2022062422/56649ef05503460f94c001ff/html5/thumbnails/14.jpg)
Example 3Determine Line Relationships
Answer: The lines are neither parallel nor perpendicular.
Check When graphed, you can see that the lines arenot parallel and do not intersect in right angles.
![Page 15: 3-3 Slopes of Lines. CCSS Content Standards G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems](https://reader036.vdocument.in/reader036/viewer/2022062422/56649ef05503460f94c001ff/html5/thumbnails/15.jpg)
Example 3
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)
![Page 16: 3-3 Slopes of Lines. CCSS Content Standards G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems](https://reader036.vdocument.in/reader036/viewer/2022062422/56649ef05503460f94c001ff/html5/thumbnails/16.jpg)