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Coordinate Geometry

Coordinate Geometry. Adapted from the Geometry Presentation by Mrs. Spitz Spring 2005. http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.3%20Proving%20Quads%20are%20Parallelograms.ppt. Using Coordinate Geometry.

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Coordinate Geometry

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  1. CoordinateGeometry Adapted from the Geometry Presentation by Mrs. Spitz Spring 2005 http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.3%20Proving%20Quads%20are%20Parallelograms.ppt

  2. Using Coordinate Geometry • When a figure is in the coordinate plane, you can use the Distance Formula to prove that sides are congruent and you can use the Slope Formula to prove sides are parallel or perpendicular. http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.3%20Proving%20Quads%20are%20Parallelograms.ppt

  3. Show that A(2, -1), B(1, 3), C(6, 5) and D(7,1) are the vertices of a parallelogram. Ex: Using properties of parallelograms http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.3%20Proving%20Quads%20are%20Parallelograms.ppt

  4. Method 1—Show that opposite sides have the same slope, so they are parallel. Slope of AB. 3-(-1) = - 4 1 - 2 Slope of CD. 1 – 5 = - 4 7 – 6 Slope of BC. 5 – 3 = 2 6 - 1 5 Slope of DA. - 1 – 1 = 2 2 - 7 5 AB and CD have the same slope, so they are parallel. Similarly, BC ║ DA. Ex: Using properties of parallelograms Because opposite sides are parallel, ABCD is a parallelogram. http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.3%20Proving%20Quads%20are%20Parallelograms.ppt

  5. Method 2—Show that opposite sides have the same length. AB=√(1 – 2)2 + [3 – (- 1)2] = √17 CD=√(7 – 6)2 + (1 - 5)2 = √17 BC=√(6 – 1)2 + (5 - 3)2 = √29 DA= √(2 – 7)2 + (-1 - 1)2 = √29 AB ≅ CD and BC ≅ DA. Because both pairs of opposites sides are congruent, ABCD is a parallelogram. Ex: Using properties of parallelograms http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.3%20Proving%20Quads%20are%20Parallelograms.ppt

  6. Method 3—Show that one pair of opposite sides is congruent and parallel. Slope of AB = Slope of CD = -4 AB=CD = √17 AB and CD are congruent and parallel, so ABCD is a parallelogram. Ex: Using properties of parallelograms http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.3%20Proving%20Quads%20are%20Parallelograms.ppt

  7. Show that ABCD is a trapezoid. Compare the slopes of opposite sides. The slope of AB = 5 – 0 = 5 = - 1 0 – 5 -5 The slope of CD = 4 – 7 = -3 = - 1 7 – 4 3 The slopes of AB and CD are equal, so AB ║ CD. The slope of BC = 7 – 5 = 2 = 1 4 – 0 4 2 The slope of AD = 4 – 0 = 4 = 2 7 – 5 2 The slopes of BC and AD are not equal, so BC is not parallel to AD. So, because AB ║ CD and BC is not parallel to AD, ABCD is a trapezoid. Ex: Using properties of trapezoids http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

  8. Homework • Work Packet: WORKSHEET

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