6 6 Lesson Properties of Kites and Trapezoids

6 -6 Lesson Properties of Kites and Trapezoids #88: Quadrilaterals Take out your HW Holt Geometry

6 -6 Properties of Kites and Trapezoids Big Ideas Page 364 Holt Geometry

6 -6 Properties of Kites and Trapezoids Holt Geometry

6 -6 Properties of Kites and Trapezoids Holt Geometry

6 -6 Properties of Kites and Trapezoids Holt Geometry

6 -6 Properties of Kites and Trapezoids . Holt Geometry

6 -6 Properties of Kites and Trapezoids . Holt Geometry

6 -6 Properties of Kites and Trapezoids Refresher: What is a polygon? A closed figure made up of at least 3 line segments that only intersect at their endpoints. What is a quadrilateral? A polygon that has 4 sides Holt Geometry

6 -6 Properties of Kites and Trapezoids Properties of a Quadrilateral 1. A four sided polygon Holt Geometry

Quadrilateral Family Tree 6 -6 Properties of Kites and Trapezoids Quadrilaterals Kite Trapezoid Isosceles Trapezoid The following family tree applies to all quadrilaterals (4 sided polygons). Parallelogram Rectangle Rhombus Square EACH SHAPE HAS THE PROPERTIES OF THE SHAPE ABOVE IT! Holt Geometry

6 -6 Properties of Kites and Trapezoids s Holt Geometry g e Le gl an Leg angle s A trapezoid is a quadrilateral with at least one pair of parallel sides. Each of the parallel sides is called a base. The nonparallel sides are called legs. Base angles of a trapezoid are two consecutive angles whose common side is a base.

6 -6 Properties of Kites and Trapezoids Different types of trapezoids: Holt Geometry

6 -6 Properties of Kites and Trapezoids Properties of a Trapezoid 1. It is a Quadrilateral 2. It has at least one pair of opposite sides parallel 3. It has supplementary “leg angles” Holt Geometry

6 -6 Properties of Kites and Trapezoids If the legs of a trapezoid are congruent, the trapezoid is an isosceles trapezoid. The legs of a trapezoid are the nonparallel sides The following theorems state the properties of isosceles trapezoids. Holt Geometry

6 -6 Properties of Kites and Trapezoids Holt Geometry

6 -6 Properties of Kites and Trapezoids Properties of an Isosceles Trapezoid 1. It is a quadrilateral 2. It is a trapezoid 3. It has congruent legs 4. It has congruent base angles 5. It has congruent diagonals Holt Geometry

6 -6 Try Properties Kitesnotebook! and Trapezoids this inofyour Example 1 Find m A. m C + m B = 180° 100 + m B = 180 m B = 80° A B m A = m B m A = 80° Holt Geometry

6 -6 Properties of Kites and Trapezoids Example 2 JN = 10. 6, and NL = 14. 8. Find KM. KM = JL JL = JN + NL KM = 10. 6 + 14. 8 = 25. 4 Holt Geometry

6 -6 Properties. Try of Kites Thisand ! Trapezoids Example 3 Find the value(s) of “a” so that PQRS is isosceles. S P m S = m P 2 a 2 – 54 = a 2 + 27 a 2 = 81 a = 9 or a = – 9 Holt Geometry

6 -6 Properties of Kites and Trapezoids The midsegment of a trapezoid is the segment whose endpoints are the midpoints of the legs. Holt Geometry

6 -6 Properties. Try of Kites Thisand ! Trapezoids Example 4 Find EF. EF = 10. 75 Holt Geometry

6 -6 Properties HW of Kites #88 and Trapezoids HAVE A GREAT DAY! Big Ideas Page 403 2, 7 -12, 19, 31 Interior/Exterior Angle quiz tomorrow! Holt Geometry