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Trapezoids and Kites.

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1 Trapezoids and Kites

2 Essential Questions How do I use properties of trapezoids?
How do I use properties of kites?

3 Vocabulary Trapezoid – a quadrilateral with exactly one pair of parallel sides. A trapezoid has two pairs of base angles. In this example the base angles are A & B and C & D leg base

4 Base Angles Trapezoid Theorem
If a trapezoid is isosceles, then each pair of base angles is congruent.  A   B,  C   D

5 Base Angles Trapezoid Converse
If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid. ABCD is an isosceles trapezoid

6 Diagonals of a Trapezoid Theorem
A trapezoid is isosceles if and only if its diagonals are congruent.

7 Example 1 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 )

8 Definition Midsegment of a trapezoid – the segment that connects the midpoints of the legs.

9 Midsegment Theorem for Trapezoids
The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.

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

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

12 Theorem: Opposite Angles of a Kite
If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent A  C, B  D

13 Example 2 Find the side lengths of the kite.

14 Example 2 Continued We can use the Pythagorean Theorem to find the side lengths. = (WX)2 = (WX)2 544 = (WX)2 = (XY)2 = (XY)2 288 = (XY)2

15 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

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

17 Homework Pages 2- 14 evens Page 333 6 – 12 all


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