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Trapezoids and Kites

Trapezoids and Kites. Geometry Unit 12, Day 5 Mr. Zampetti. Adapted from a PowerPoint created by Mrs. Spitz. http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt. A trapezoid is a quadrilateral with exactly one pair of parallel sides.

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Trapezoids and Kites

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  1. Trapezoids and Kites Geometry Unit 12, Day 5 Mr. Zampetti Adapted from a PowerPoint created by Mrs. Spitz http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

  2. A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are the bases. Using properties of trapezoids http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

  3. A trapezoid has two pairs of base angles. For instance in trapezoid ABCD D and C are one pair of base angles. The other pair is A and B. The nonparallel sides are the legs of the trapezoid. Using properties of trapezoids http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

  4. If the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid. Using properties of trapezoids http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

  5. Theorem 9-16 If a trapezoid is isosceles, then each pair of base angles is congruent. A ≅ B, C ≅ D Trapezoid Theorems http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

  6. Theorem 9-17 A trapezoid is isosceles if and only if its diagonals are congruent. ABCD is isosceles if and only if AC ≅ BD. Trapezoid Theorems http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

  7. PQRS is an isosceles trapezoid. Find mP, mQ, mR. mR = mS = 50°. mP = 180°- 50° = 130°, and mQ = mP = 130° Ex: Using properties of Isosceles Trapezoids 50° You could also add 50 and 50, get 100 and subtract it from 360°. This would leave you 260/2 or 130°. http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

  8. A kite is a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent. Using properties of kites http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

  9. Theorem 9-18 If a quadrilateral is a kite, then its diagonals are perpendicular. AC  BD Kite theorems http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

  10. WXYZ is a kite so the diagonals are perpendicular. You can use the Pythagorean Theorem to find the side lengths. WX = WZ = √202 + 122≈ 23.32 XY = YZ = √122 + 122≈ 16.97 Ex. 4: Using the diagonals of a kite http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

  11. Venn Diagram: http://teachers2.wcs.edu/high/rhs/staceyh/Geometry/Chapter%206%20Notes.ppt#435,22,6.2 – Properties of Parallelograms

  12. Flow Chart: http://www.quia.com/pop/103618.html?AP_rand=172732766

  13. Properties of Quadrilaterals • http://www.quia.com/pop/103618.html?AP_rand=172732766

  14. Homework: • Work Packet: Trapezoids and Kites http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

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