Pre-Algebra 5-5 Coordinate Geometry 5-5 Coordinate Geometry Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Pre-Algebra 5-5 Coordinate Geometry Warm Up Complete each sentence. 1. Two lines in a plane that never meet are called lines. 2. lines intersect at right angles. 3. The symbol || means that lines are. 4. When a transversal intersects two lines, all of the acute angles are congruent. parallel Perpendicular parallel Pre-Algebra 5-5 Coordinate Geometry parallel

Pre-Algebra 5-5 Coordinate Geometry Problem of the Day What type of polygon am I? My opposite angles have equal measure. I do not have a right angle. All my sides are congruent. rhombus

Pre-Algebra 5-5 Coordinate Geometry Learn to identify polygons in the coordinate plane.

Pre-Algebra 5-5 Coordinate Geometry Vocabulary slope rise run

Pre-Algebra 5-5 Coordinate Geometry In computer graphics, a coordinate system is used to create images, from simple geometric figures to realistic figures used in movies. Properties of the coordinate plane can be used to find information about figures in the plane, such as whether lines in the plane are parallel.

Pre-Algebra 5-5 Coordinate Geometry Slope is a number that describes how steep a line is.

Pre-Algebra 5-5 Coordinate Geometry The slope of a horizontal line is 0. The slope of a vertical line is undefined. slope = vertical change horizontal change = rise run

Pre-Algebra 5-5 Coordinate Geometry Additional Example 1A: Finding the Slope of a Line Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. A. XY positive slope; slope of XY = = –5 –4 5454

Pre-Algebra 5-5 Coordinate Geometry Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. B. ZA negative slope; slope of ZA = = – – Additional Example 1B: Finding the Slope of a Line

Pre-Algebra 5-5 Coordinate Geometry Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. C. BC slope of BC is undefined Additional Example 1C: Finding the Slope of a Line

Pre-Algebra 5-5 Coordinate Geometry Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. D. DM slope of DM = 0 Additional Example 1D: Finding the Slope of a Line

Pre-Algebra 5-5 Coordinate Geometry Try This: Example 1A Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. A. AB A C B D F E H G positive slope; slope of AB = 1 8

Pre-Algebra 5-5 Coordinate Geometry B. CD slope of CD is undefined Try This: Example 1B Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. A C B D F E H G

Pre-Algebra 5-5 Coordinate Geometry C. EF slope of EF = 0 Try This: Example 1C Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. A C B D F E H G

Pre-Algebra 5-5 Coordinate Geometry D. GH Try This: Example 1D Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. A C B D F E H G negative slope; slope of GH = = – –

Pre-Algebra 5-5 Coordinate Geometry Slopes of Parallel and Perpendicular Lines Two lines with equal slopes are parallel. Two lines whose slopes have a product of –1 are perpendicular.

Pre-Algebra 5-5 Coordinate Geometry Additional Example 2: Finding Perpendicular Line and Parallel Lines Which lines are parallel? Which lines are perpendicular? slope of EF = 3232 slope of GH = 3535 slope of PQ = 3535 slope of QR = or –1 3 – slope of CD = or – –2 3

Pre-Algebra 5-5 Coordinate Geometry Additional Example 2 Continued The slopes are equal. = The slopes have a product of –1: – = – GH || PQ EF  CD Which lines are parallel? Which lines are perpendicular?

Pre-Algebra 5-5 Coordinate Geometry Try This: Example 2 A C B D F E K J H G Which lines are parallel? Which lines are perpendicular? slope of AB = or –6 4 –3 2 slope of CD = –2 3 slope of EF = or –4 6 –2 3 slope of GH = 2323 slope of JK = or 1 3

Pre-Algebra 5-5 Coordinate Geometry CD || EF GH  AB A C B D F E K J H G Try This: Example 2 Continued Which lines are parallel? Which lines are perpendicular? The slopes are equal. = –2 3 –2 3 The slopes have a product of –1: – = –

Pre-Algebra 5-5 Coordinate Geometry Additional Example 3A: Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. A. A(3, –2), B(2, –1), C(4, 3), D(5, 2) parallelogram CD || BA and BC || AD

Pre-Algebra 5-5 Coordinate Geometry B. R(–3, 1), S(–4, 2), T(–3, 3), U(–2, 2) parallelogram, rectangle, rhombus, square Additional Example 3B: Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. TU || SR and ST || RU TURU, RURS, RSST and STTU

Pre-Algebra 5-5 Coordinate Geometry C. G(1, –1), H(1, –2), I(3, –3), J(3, 1) trapezoid Additional Example 3C: Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. GH || JI

Pre-Algebra 5-5 Coordinate Geometry D. W(2, –3), X(3, –4), Y(6, –1), Z(5, 0) parallelogram, rectangle Additional Example 3D: Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. WZ || XY and WX || ZY WZZY, ZYXY, XYWX and WXWZ

Pre-Algebra 5-5 Coordinate Geometry Try This: Example 3A Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. A. A(–1, 3), B(1, 5), C(7, 5), D(5, 3) parallelogram A C B D CD || BA and BC || AD

Pre-Algebra 5-5 Coordinate Geometry B. E(1, 5), F(7, 5), G(6, 1), H(2, 1) trapezoid E F H G EF || HG Try This: Example 3B Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.

Pre-Algebra 5-5 Coordinate Geometry C. W(4, 8), X(8, 2), Y(2, –2), Z(–2, 4) parallelogram, rectangle, rhombus, square X W Y Z ZW || YX and WX || ZY WXZW, XYWX, YZXY and ZWYZ Try This: Example 3C Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.

Pre-Algebra 5-5 Coordinate Geometry D. R(–1, 1), S(3, 7), T(6, 5), U(2, –1) parallelogram, rectangle R S U T TU || SR and ST || RU TURU, RURS, RSST and STTU Try This: Example 3D Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.

Pre-Algebra 5-5 Coordinate Geometry Lesson Quiz Determine the slope of each line. 1. PQ 2. MN 3. MQ 4. NP 5. Which pair of lines are parallel? – 10 3 MN, RQ