Please read the following and consider yourself in it. An Affirmation Please read the following and consider yourself in it. I am capable of learning. I can accomplish mathematical tasks. I am ultimately responsible for my learning.
Standards MGSE9-12.G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. (Focus on quadrilaterals, right triangles, and circles.) MGSE9-12.G.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). MGSE9-12.G.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. MGSE9-12.G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
Objectives MGSE9-12.G.GPE.5 SWBAT Prove the slope criteria for parallel and perpendicular lines IOT solve geometric problems. SWBAT Apply slope criteria IOT synthesize the equation of a line parallel or perpendicular to a given line that passes through a given point.
containing the point (5, –2) in point-slope form? B. C. D. 5-Minute Check 1
containing the point (5, –2) in point-slope form? B. C. D. 5-Minute Check 1
What is the equation of the line with slope 3 containing the point (–2, 7) in point-slope form? A. y = 3x + 7 B. y = 3x – 2 C. y – 7 = 3x + 2 D. y – 7 = 3(x + 2) 5-Minute Check 2
What is the equation of the line with slope 3 containing the point (–2, 7) in point-slope form? A. y = 3x + 7 B. y = 3x – 2 C. y – 7 = 3x + 2 D. y – 7 = 3(x + 2) 5-Minute Check 2
What equation represents a line with slope –3 containing the point (0, 2.5) in slope-intercept form? A. y = –3x + 2.5 B. y = –3x C. y – 2.5 = –3x D. y = –3(x + 2.5) 5-Minute Check 3
What equation represents a line with slope –3 containing the point (0, 2.5) in slope-intercept form? A. y = –3x + 2.5 B. y = –3x C. y – 2.5 = –3x D. y = –3(x + 2.5) 5-Minute Check 3
What equation represents a line containing points (1, 5) and (3, 11)? A. y = 3x + 2 B. y = 3x – 2 C. y – 6 = 3(x – 2) D. y – 6 = 3x + 2 5-Minute Check 5
What equation represents a line containing points (1, 5) and (3, 11)? A. y = 3x + 2 B. y = 3x – 2 C. y – 6 = 3(x – 2) D. y – 6 = 3x + 2 5-Minute Check 5
A. B. C. D. 5-Minute Check 6
A. B. C. D. 5-Minute Check 6
G.CO.9 Prove theorems about lines and angles. Content Standards G.CO.9 Prove theorems about lines and angles. G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. CCSS
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D. It is not possible to prove any of the lines parallel. A. Given 1 5, is it possible to prove that any of the lines shown are parallel? A. Yes; ℓ ║ n B. Yes; m ║ n C. Yes; ℓ ║ m D. It is not possible to prove any of the lines parallel. Example 1
D. It is not possible to prove any of the lines parallel. A. Given 1 5, is it possible to prove that any of the lines shown are parallel? A. Yes; ℓ ║ n B. Yes; m ║ n C. Yes; ℓ ║ m D. It is not possible to prove any of the lines parallel. Example 1
D. It is not possible to prove any of the lines parallel. B. Given m4 = 105 and m5 = 70, is it possible to prove that any of the lines shown are parallel? A. Yes; ℓ ║ n B. Yes; m ║ n C. Yes; ℓ ║ m D. It is not possible to prove any of the lines parallel. Example 1
D. It is not possible to prove any of the lines parallel. B. Given m4 = 105 and m5 = 70, is it possible to prove that any of the lines shown are parallel? A. Yes; ℓ ║ n B. Yes; m ║ n C. Yes; ℓ ║ m D. It is not possible to prove any of the lines parallel. Example 1
Find mZYN so that || . Show your work. Use Angle Relationships Find mZYN so that || . Show your work. Read the Test Item From the figure, you know that mWXP = 11x – 25 and mZYN = 7x + 35. You are asked to find mZYN. Example 2
m WXP = m ZYN Alternate exterior angles Use Angle Relationships Solve the Test Item WXP and ZYN are alternate exterior angles. For line PQ to be parallel to line MN, the alternate exterior angles must be congruent. So mWXP = mZYN. Substitute the given angle measures into this equation and solve for x. Once you know the value of x, use substitution to find mZYN. m 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. Example 2
Now use the value of x to find mZYN. Use Angle Relationships Now use the value of x to find mZYN. mZYN = 7x + 35 Original equation = 7(15) + 35 x = 15 = 140 Simplify. Answer: Example 2
Now use the value of x to find mZYN. Use Angle Relationships Now use the value of x to find mZYN. mZYN = 7x + 35 Original equation = 7(15) + 35 x = 15 = 140 Simplify. Answer: mZYN = 140 Check Verify the angle measure by using the value of x to find mWXP. mWXP = 11x – 25 = 11(15) – 25 = 140 Since mWXP = mZYN, WXP ZYN and || . Example 2
ALGEBRA Find x so that || . A. x = 60 B. x = 9 C. x = 12 D. x = 12 Example 2
ALGEBRA Find x so that || . A. x = 60 B. x = 9 C. x = 12 D. x = 12 Example 2
Prove Lines Parallel CONSTRUCTION In the window shown, the diamond grid pattern is constructed by hand. Is it possible to ensure that the wood pieces that run the same direction are parallel? If so, explain how. If not, explain why not. Answer: Example 3
Prove Lines Parallel CONSTRUCTION In the window shown, the diamond grid pattern is constructed by hand. Is it possible to ensure that the wood pieces that run the same direction are parallel? If so, explain how. If not, explain why not. Answer: Measure the corresponding angles formed by two consecutive grid lines and the intersecting grid line traveling in the opposite direction. If these angles are congruent, then the grid lines that run in the same direction are parallel by the Converse of the Corresponding Angles Postulate. Example 3