EQ: GPE.4 How do I calculate distance, midpoint, and slope?
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1 EQ: GPE.4 How do I calculate distance, midpoint, and slope? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 3, Lesson 1 1. Warm Up 2. G.CO.12 quiz 3. TI Nspire activity 4. Closure 20 Distance, Slope, and Midpoint 21 Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm u Warm Up: 1. Using the scratch paper and using a straight edge, draw each of the following: a segment (any length) an acute angle Now, Now, switch your paper with another person. 2. Construct a segment that is congruent to the original. 3. Construct an angle that is congruent to the original. 4. Construct the perpendicular bisector of the original segment. 5. Construct the angle bisector of the original angle. 1
2 2
3 G.CO.12 Quiz! 3
4 ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity Length Midpoint Slope 4
5 Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Right Side... Write a summary that answers the essential question. Left Side... Explain the difference between slope and distance. 5
6 EQ: GPE.5 How do I identify parallel and perpendicular lines? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 3, Lesson 2 1. Warm Up 2. GPE.4 Quiz 3. Notes 4. Left Side Practice 5. Closure 22 Parallell and Perpendicular lines 23 Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm u Warm Up: Given point P(4,2) and point R( 3, 3). Graph the points. Then, calculate the following: 1) the distance between P and R. 2) the slope of PR. 3) the midpoint between P and R. 4.) 6
7 GPE.4 Quiz! 7
8 notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes Parallel Lines Perpendicular Lines Lines that never intersect. Two lines that are parallel have the same slope 2 lines that intersect at a 90 angle. Two lines that are perpendicular have slopes that are negative reciprocals. (the product of their slopes is 1) notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes Summary: Ex: Given line c with a slope of 2, what is the slope of the line parallel to it? Perpendicular to it? 8
9 ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity Left Side Practice For each of the following, (a) identify the slope of the given equation (b) write the slope of a line parallel to that line (c) write the slope of a line perpendicular to that line 1. y = 3x y = 2/3x 4 3. y = 2 5/4x ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity *How would I draw a line perpendicular to this one? 6. 2x + 3y = x 2y = x 3y = x + 2y = 8 Extra Practice: Given the following points, are the two lines parallel, perpendicular, or neither? Line AB: A(2,0) B(4, 2) Line FG: F(5,1) G(0, 4) 9
10 Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Right Side... Write a summary that answers the essential question. Left Side... Looking ONLY at the slopes, how do you tell when two lines are parallel and when two lines are perpendicular? 10
11 EQ: GPE.5 How do I graph lines using my calculator? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 3, Lesson 3 1. Warm Up 2. Notes 3. Rotations 4. Closure 24 Graph lines with a Calculator 25 Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm u Warm Up: 3. What are the slopes of the lines shown at the right? 4.) W is between U and X, V is between U and W, X is between V and Y, UY = 24, WY = 14, and UV = VW = WX. What is the length of XY? 11
12 notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes Graphing lines on your calculator Open up a new document Then, choose 2: Add Graphs Menu > 3: Graph Entry/Edit > 2: Equation > 1: Line y = 2x + 6 2x + 4y = 4 What is the slope and y intercept for each line? notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes notes Ex: Graph the following lines. Then, find the slope and y intercept for each. 1. y = 3x x + 2y = y + 5x = 30 *changing your window *ctrl Z to undo your last command Ex: Are the following two lines parallel, perpendicular, or intersecting? Explain. 5. 4y + 3x = 16 y = 4/3x x + 5y = 10 y = 2/5x 3 Summary: 12
13 y ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity 13
14 Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Right Side... Write a summary that answers the essential question. Left Side... Explain two different ways to find the distance between these two points. 14
15 EQ: G.CO.9 What pattern forms when two parallel lines are cut by a transversal? Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Essential Question Week 3, Lesson 4 1. Warm Up 2. GPE.5 Quiz 3. TI NSpire activity 4. Closure 26 Parallel lines cut by a transversal 27 Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm up Warm u Warm Up: 1. Given the line 5x 2y = 12, (a) write the slope of this line. (b) write the slope of the line parallel to this line. (c) write the slope of the line perpendicular to this line. 2. Given the line below, (a) write the slope of this line. (b) write the slope of the line parallel to this line. (c) write the slope of the line perpendicular to this line. ( 5, 2) (5, 5) 15
16 GPE.5 Quiz 16
17 ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ss Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity ICA: In Class Activity 17
18 Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Closure Right Side... Write a summary that answers the essential question. Left Side... Solve for x and find the measure of each angle. 18
19 19
EQ: G.CO.4 How do I reflect over parallel and perpendicular lines?
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