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Trapezoids and Kites

Explore the properties of trapezoids and kites, key shapes in geometry. A trapezoid, a quadrilateral with one pair of parallel sides, features base angles and legs that contribute to its classification as isosceles if its legs are congruent. Discover theorems relating to their angles and diagonals. A kite, another quadrilateral with two pairs of consecutive congruent sides, has perpendicular diagonals. This unit provides engaging activities and Venn diagrams to help students grasp these concepts thoroughly.

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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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