1. Lesson 6 – 6 Trapezoids and Kites
Geometry
Lesson 6 – 6
Trapezoids and Kites
Objective:
Apply properties of trapezoids.
Apply properties of kites.

2. Trapezoid What is a trapezoid?
A quadrilateral with exactly one pair of parallel sides.
Bases – the parallel sides
Legs – the nonparallel sides
Base angles – the angles formed by the base and one of the legs
Isosceles trapezoid
congruent legs

3. Theorem
Theorem 6.21
If a trapezoid is isosceles, then each pair of base angles is congruent.

4. Theorem
Theorem 6.22
If a trapezoid has one pair of congruent base angles, then it is an isosceles trapezoid.

5. Theorem
Theorem 6.23
A trapezoid is isosceles if and only if its diagonals are congruent.

6. The speaker shown is an isosceles trapezoid. If m FJH = 85, FK = 8 in
The speaker shown is an isosceles trapezoid. If m FJH = 85, FK = 8 in. and JG = 19 in. Find each measure. KH 95
8 in 19 95 85 85
8 + KH = 19
FH = JG
KH = 11
FH = 19
FK + KH = 19

7. WXYZ is
Isosceles trap.
10 cm
15 cm 45 XZ XV 45
135
25 cm
10 cm

8. To be a trapezoid the quad must have one set of parallel sides.
Quadrilateral ABCD has vertices A (-3, 4) B (2, 5) C (3, 3) and D (-1, 0). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid.
To be a trapezoid the quad must
have one set of parallel sides.
Slope of AD = -2
Slope of BC = -2
The figure is a trapezoid
(AB and DC obviously not parallel)
To be isosceles the diagonals must be congruent.
Trapezoid ABCD is not an isosceles trapezoid.

9. Quadrilateral QRST has vertices
Q(8, -4) R(0, 8) S(6, 8) T (-6, -10). Determine whether it is an isosceles trapezoid.
Slope of QR = 3/2
Slope of RS = 0
Slope of QT = 3/7
Slope of TS = 3/2
Since one pair of parallel sides QRST is a trapezoid.
Trapezoid QRST is not an isosceles trapezoid.

10. Midsegment of a Trapezoid
The segment that connects the midpoints of the legs of the trapezoid.

11. Theorem Trapezoid Midsegment Theorem
The midsegment of a trapezoid is parallel to each base and its measure is one half the sum of the lengths of the bases.

12. In the figure segment LH is the midsegment of trapezoid FGJK
In the figure segment LH is the midsegment of trapezoid FGJK. What is the value of x?
(2)
(2)
30 = x
11.8 = x

13. G is the midpoint of segment DC. The x-coordinate is 10.5
Trapezoid ABCD is shown below. If FG II AD, what is the x-coordinate of point G?
G is the midpoint of
segment DC.
The x-coordinate is 10.5

14. Kite
A quadrilateral with exactly two pairs of consecutive congruent sides.

15. Theorem
Theorem 6.25
If a quadrilateral is a kite, then its diagonals are perpendicular.
Where else have learned about the diagonals being perpendicular?
Square & Rhombus
Why does this work for all 3 figures?
Is a Square and a Rhombus considered a Kite?

16. Theorem
Theorem 6.26
If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent.

17. pair of opposite congruent angles x x
If FGHJ is a kite, find the measure of angle GFJ
Kites have exactly one
pair of opposite congruent
angles x x
2x = 360
2x = 360
2x = 160
x = 80

18. If WXYZ is a kite, find ZY. (PZ)2 + (PY)2 = (ZY)2 82 + 242 = (ZY)2
Remember to simplify!

19. x 50 x 38
2x = 360
2x + 88 = 360
2x = 272
x = 136

20. 5 8 If BT = 5 and TC = 8, find CD. (BT)2 + (TC)2 = (BC)2
BC = CD

21. Homework
Pg – 7 all, 8 – 24 EOE, 36 – 48 EOE, 66, 70 – 76 E, 82