1. 7.4 Trapezoids and Kites Objectives:
• Definitions of trapezoid and kite.
• Properties of trapezoids and kites.

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

3. Example 1 PQRS is an isosceles trapezoid. Find mLP, mLQ and mLR.
MLR = 50º since base angles are congruent
mLP = 130º and mLQ = 130º

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

5. Concept: Vertex Angles
Vertex angles: Angles formed between the two congruent sides.
Vertex angles

6. Concept: Non-Vertex Angles
Non-Vertex angles: Angles formed between the two non-congruent sides. Non-vertex angles are congruent,
Non-Vertex
angles

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

8. Concept: Opposite Angles of a Kite
If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent
LA = LC, LB ≠ LD

9. Example 2
Find the side lengths of the kite.

10. Example 2 Cont…
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

11. Example 3 Find mLG and mLJ. Since GHJK is a kite, LG = LJ
So 2(mLG) + 132º + 60º = 360º
2(mLG) =168º
mLG = 84º and mLJ =84º

12. Concept: Try This! RSTU is a kite. Find mR, mS and mT.
x x = 360
2x = 360
2x = 80
x = 40
So mLR = 70º, mLT = 40º and mLS = 125º

13. Homework
Practice Master 7.4