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Parallel and Perpendicular Lines BIG PICTURE of this UNIT: November 09, 2015 • mastery with algebraic skills to be used in our work with co-ordinate geometry (midpoint, length, slope) • understanding various geometric properties of quadrilaterals & triangles • how do you really prove that something is “true”? Where we’ve been Where we are You know about geometric figures CONTEXT of this LESSON: and now you know how to find a midpoint and length IM1 Becoming proficient with another analytical tool that we can use in coordinate geometry: parallel and perpendicular lines Where we are heading How can I prove various geometric properties of quadrilaterals and triangles? Parallel and Perpendicular Lines Lesson Objectives: 1. 2. IM1 Exploring parallel lines and their proper3es. Exploring perpendicular lines and their proper3es. November 09, 2015 Parallel and Perpendicular Lines November 09, 2015 Warm-up IM1 1. Solve the following equation for x. 2. Determine the midpoint and length of the line segment formed between (2, 3), and (-8, 9). Draw a picture! Parallel and Perpendicular Lines November 09, 2015 We are going to use the GeoGebra App (search GeoGebra in your web browser to explore parallel and perpendicular. Click "Algebra" once you are in the App. IM1 Parallel and Perpendicular Lines November 09, 2015 Pick two points A and B Record the points in the table below Draw a line segment between them and determine the slope of the line segment between those points. Now Find another two points that create a PARALLEL line to the one you just made. Do this 6 different 3mes Point A Point B Slope of AB Point C Point D Slope of CD Observations: IM1 Parallel and Perpendicular Lines November 09, 2015 Given the three points A, B, C… I want you to find the fourth point D such that line segment AB is Parallel to line segment CD Point A (2,5) (3,6) (-5,-4) (-2,-8) (3,7) (-2,9) (0,-7) Point B (4,7) (0,-2) (7,-1) (-8,6) (-4,2) (-6,2) (5,0) Point C (-3,-2) (1,1) (0,5) (0,0) (-2,1) (5,0) (2,3) Point D IM1 Parallel and Perpendicular Lines November 09, 2015 Exploring Perpendicularism using dynamic geometry so5ware: GeoGebra Define perpendicular in your own words: Draw a picture of perpendicular lines: Draw 4 shapes that you KNOW have perpendicular lines: IM1 Parallel and Perpendicular Lines November 09, 2015 Pick two points A and B. Record the points in the table below. Draw a line segment between them and determine the slope of the line segment between those points. Now Find another two points that create a perpendicular line to the one you just made. Do this 6 different 3mes. Do your best to “eyeball” it…get as close as you can. Determine the slope of the new perpendicular line segment. Point A Point B Slope of AB Point C Point D Slope of CD IM1 Parallel and Perpendicular Lines November 09, 2015 The following points AB and CD WILL create perpendicular line segments. Explore the three examples in GeoGebra and see what you can determine about perpendicular lines and their slopes. Point A (1,1) (-3,-1) (-2,3) Point B (5,2) (-1,3) (2,-2) Point C (2,4) (-5,3) (-2,-3) Point D (3,0) (3,-1) (3,1) Slope of AB Slope of CD Observations: IM1 Parallel and Perpendicular Lines November 09, 2015 Given the points A(2,3) B(5,8) C(10,5) and D(7,0) create the line segments AB, BC, CD, DA and then discuss what kind of shape this makes. Can you be certain of the shape that it makes? Could you prove your ideas? Draw a picture of your GeoGebra below. IM1