Lesson 5.3 Trapezoids and Kites Homework: 5.3/1-8,19 QUIZ Wednesday 5.1 – 5.4

PROCEDURES for today: 1. OPEN TEXTBOOKS 2. Tools – patty paper(2), protractor, ruler 3. INVESTIGATIONs 1 & 2 – ALL steps 4. Complete the 4 kite conjectures & the 3 trapezoid conjectures

Definition Kite – a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.

Parts of a Kite Vertex angles: <B & <D Vertex diagonal BD Non-Vertex diagonal CA Non-Vertex angles: <A & <C

Properties of Kites The diagonals of a kite are perpendicular Non-vertex angles (a)are congruent Vertex diagonal bisects the vertex angles non-vertex diagonal

Perpendicular Diagonals of a Kite If a quadrilateral is a kite, then its diagonals are perpendicular.

Non-Vertex Angles of a Kite If a quadrilateral is a kite, then non- vertex angles are congruent A  C, B  D

Vertex diagonals bisect vertex angles If a quadrilateral is a kite then the vertex diagonal bisects the vertex angles.

Vertex diagonal bisects the non-vertex diagonal If a quadrilateral is a kite then the vertex diagonal bisects the non-vertex diagonal

Definition-a quadrilateral with exactly one pair of parallel sides. Trapezoid Definition-a quadrilateral with exactly one pair of parallel sides. Base A › B Leg Leg C › D Base

Leg Angles are Supplementary Property of a Trapezoid Leg Angles are Supplementary B A › <A + <C = 180 <B + <D = 180 › C D

Isosceles Trapezoid Definition - A trapezoid with congruent legs.

Isosceles Trapezoid - Properties | | 1) Base Angles Are Congruent 2) Diagonals Are Congruent

Example PQRS is an isosceles trapezoid. Find m P, m Q and mR. m R = 50 since base angles are congruent mP = 130 and mQ = 130 (consecutive angles of parallel lines cut by a transversal are )

Find the measures of the angles in trapezoid 48 m< A = 132 m< B = 132 m< D = 48

Find BE AC = 17.5, AE = 9.6 E

Example Find the side lengths of the kite.  

Example Continued We can use the Pythagorean Theorem to find the side lengths. 122 + 202 = (WX)2 144 + 400 = (WX)2 544 = (WX)2 122 + 122 = (XY)2 144 + 144 = (XY)2 288 = (XY)2

Find the lengths of the sides of the kite W 4 Z X 5 5 8 Y

Find the lengths of the sides of kite to the nearest tenth 2 4 7 2

Example 3 Find mG and mJ. Since GHJK is a kite G  J So 2(mG) + 132 + 60 = 360 2(mG) =168 mG = 84 and mJ = 84

Try This! RSTU is a kite. Find mR, mS and mT. x +30 + 125 + 125 + x = 360 2x + 280 = 360 2x = 80 x = 40 So mR = 70, mT = 40 and mS = 125

Try These 2. m<C = x +12 and m<B = 3x – 2, find x and the measures of the 2 angles 1. If <A = 134, find m<D x = 42.5 m<C = 54.5 m<B = 125.5 m<D = 46

Using Properties of Trapezoids When working with a trapezoid, the height may be measured anywhere between the two bases.  Also, beware of "extra" information.  The 35 and 28 are not needed to compute this area. Area of trapezoid = Find the area of this trapezoid. A = ½ * 26 * (20 + 42) A = 806

Using Properties of Trapezoids Example 2 Find the area of a trapezoid with bases of 10 in and 14 in, and a height of 5 in.

Area Kite = one-half product of diagonals Using Properties of Kites Area Kite = one-half product of diagonals

a) Find the lengths of all the sides. Using Properties of Kites Example 6 ABCD is a Kite. a) Find the lengths of all the sides. 2 4 4 E 4 Find the area of the Kite.

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

Flow Chart:

Homework