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Transcript
CC Geometry H Aim #15: How do we apply the properties of quadrilaterals in coordinate geometry proofs? Do Now: ΔAFN: A(-7,6), F(-1,6), N(-4,2). Prove the triangle is isosceles, but not equilateral. Use of graph is optional. Label your work and write a concluding statement. 1) One method to prove a quadrilateral is a parallelogram is to prove the diagonals bisect each other: Show that the diagonals have the same midpoint. Write a concluding statement. 2) Given a quadrilateral with vertices E(0,5), F(6,5), G(4,0) and H(-2,0). a) Prove that EFGH is a parallelogram by showing that both pairs of opposite sides are parallel (a second method). Use of the grid is optional. Write a concluding statement. b) Prove (2,2.5) is the intersection point of both diagonals of this quadrilateral. 3) Given quadrilateral JKLM with vertices J(-4,2), K(1,5), L(4,0) and M(-1,-3). a) Is it a trapezoid? Prove. (If at least one pair of opposite sides is parallel, then it is a trapezoid.) b) Is it a parallelogram? Prove. c) Is it a rectangle? Prove. d) Is it a rhombus? Prove. e) Is it a square? Explain. f) Name a point on a diagonal of JKLM. Explain how you know. 4) The points O(0,0), A(-4,1), B(-3,5) and C(1,4) are the vertices of parallelogram OABC. Is this parallelogram a rectangle? Prove and write a concluding statement. Use of grid is optional. 5) A quadrilateral has vertices , , , and . Prove that the quadrilateral is a rectangle. Write a concluding statement. A guide to proving different types of quadrilaterals using coordinate geometry: 3. Prove a quadrilateral with 4 rt. angles. Slope formula 4 times. Option 4: 1. All 4 angles are equal (proving parallelogram and rectangle) 2. Diagonals are perpendicular. 1. Slope formula 4 times. 2. Slope formula 2 twice. Name: ____________________ Date: _________________ CC Geometry H HW #15 1) Complete: a) Parallel line have ________________________ slopes. b) Perpendicular lines, which form _____________ angles have _______________ __________________ slopes. c) Congruent segments have ______________ __________________. d) Segments that bisect each other share the same _________________. 2) Given a quadrilateral with vertices A(-1,3), B(1,5), C(5,1) and D(3,-1). a) Prove that ABCD is a rectangle. [Use of the grid is optional.] b) Prove that (2,2) is a point on both diagonals of the quadrilateral. 3) Prove that the quadrilateral with the vertices A(-1,4), B(2,6), (C5,4) and D(2,2) is a rhombus. 4) Prove that the quadrilateral with the vertices A(0,0), B(4,3), C(7,-1) and D(3,-4) is a square. Mixed Review: 1) In rhombus ABCD, the coordinates of the endpoints of the diagonal AC are A(-3,-2) and C(5,4). Write an equation of the line that contains diagonal BD. Using the given information, explain how you know that your line contains diagonal BD. [Use of the grid is optional.] 2) Given: Quad. TREK ≮1 is supp. to ≮4 ≮RED ≅ ≮4 Prove: parallelogram FRED statements reasons Attachments Triangle Coor HW Answer Key.pdf