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8-5 Coordinate Geometry Objective: Students identify polygons in the coordinate plane. Vocabulary Polygon- is a closed plane figure formed by three or more line segments called sides. Quadrilaterals- are polygons with four sides and four angles. Quadrilaterals Trapezoids Exactly 1 pair of parallel sides Parallelograms 2 pairs of parallel sides Rectangles Squares 4 right 4 congruent angles sides 4 congruent angles Rhombuses 4 congruent sides Slopes of Parallel and Perpendicular Lines Any two nonvertical lines with equal slopes are parallel. Any two vertical lines are parallel. Any two nonvertical lines whose slopes have a product of -1 are perpendicular. Vertical and horizontal lines are perpendicular. Example 1 Which lines are parallel? Which lines are perpendicular? Step 1 Find the slope of each line Hint: 𝒓𝒊𝒔𝒆 𝒓𝒖𝒏 Slope of 𝑃𝑄= X Q G Slope of 𝑅𝑆= Slope of 𝐴𝐵= B P Slope of 𝑃𝐴= H Slope of 𝐺𝐻= Slope of 𝑋𝑌= Step 2 Compare the slopes S R A Y Example 2 Graph the quadrilaterals with the given vertices. Give all of the names that apply to the quadrilateral. J(1,2) K(4,2) L(4,-1) M(1,-1) P(-1,2) Q(2,1) R(-1,-2) S(-3,0) 4 -1 6 -4 4 -4 Example 3 Find the coordinates of the missing vertex of square ABCD with A(4,0), B(0,4), and C(-4,0). Step 1 Graph and connect the given points Step 2 Complete the figure to find the missing vertex. 𝑨𝑩 has a slope of -1, so draw 𝑪𝑫 with a slope of -1. 𝑩𝑪 has a slope of 1, so draw 𝑨𝑫 with a slope of 1. Where do the rays intersect? 4 -4 4 -4