Trapezoids and Kites Geometry Unit 12, Day 5 Mr. Zampetti Adapted from a PowerPoint created by Mrs. Spitz

Using properties of trapezoids A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are the bases.

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.

Using properties of trapezoids If the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid.

Trapezoid Theorems Theorem 9-16 If a trapezoid is isosceles, then each pair of base angles is congruent.  A ≅  B,  C ≅  D

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.

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°.

Using properties of kites A kite is a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.

Kite theorems Theorem 9-18 If a quadrilateral is a kite, then its diagonals are perpendicular. AC  BD

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 = √ ≈ XY = YZ = √ ≈

Venn Diagram: – Properties of Parallelograms

Flow Chart:

Properties of Quadrilaterals P_rand= P_rand=

Homework: Work Packet: Trapezoids and Kites