Geometry Unit 12, Day 5 Mr. Zampetti 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

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

Using properties of trapezoids 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. http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

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

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

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

Ex: Using properties of Isosceles Trapezoids 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° 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

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

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

Ex. 4: Using the diagonals of a kite 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 http://www.taosschools.org/ths/Departments/MathDept/spitz/Courses/GeometryPPTs/6.5%20Trapezoids.ppt

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

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

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

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