1. Geometry
6.5 Trapezoids and Kites

2. Goals Know definitions of trapezoid and kite.
Use properties of them to solve problems.
December 8, 2018
6.5 Trapezoids and Kites

3. Quadrilaterals Quadrilaterals Parallelograms Rhombuses Rectangles
Some quadrilaterals are parallelograms.
Parallelograms
Rhombuses
Rectangles
Squares
December 8, 2018
6.5 Trapezoids and Kites

4. But not all… Some quadrilaterals are Trapezoids.
And some quadrilaterals are Kites.
Quadrilaterals
Parallelograms
Kites
Rhombuses
Rectangles
Trapezoids
Squares
December 8, 2018
6.5 Trapezoids and Kites

5. Trapezoid A quadrilateral with exactly one pair of parallel sides.
December 8, 2018
6.5 Trapezoids and Kites

6. Trapezoid The parallel sides are the BASES.
The non-parallel sides are the LEGS.
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6.5 Trapezoids and Kites

7. These are trapezoids:
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6.5 Trapezoids and Kites

8. Isosceles Trapezoid The legs are congruent. December 8, 2018
6.5 Trapezoids and Kites

9. Isosceles Trapezoid Theorems
6.14 Each pair of base angles is congruent.
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6.5 Trapezoids and Kites

10. Isosceles Trapezoid Theorems
6.15 If a trapezoid has one pair of congruent base angles, then the trapezoid is isosceles.
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6.5 Trapezoids and Kites

11. Isosceles Trapezoid Theorems
6.16 A trapezoid is isosceles if and only if its diagonals are congruent. B C A D
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6.5 Trapezoids and Kites

12. Problem
Find the measure of 1, 2, and 3 if the figure is an isosceles trapezoid.
75 1 3 2
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6.5 Trapezoids and Kites

13. Solution
In an isosceles trapezoid, base angles are congruent. 1 is _______.
75
75
75 1 3 2
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6.5 Trapezoids and Kites

14. The bases are parallel, so 3 = _____. 105
75
75
105 3 2
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6.5 Trapezoids and Kites

15. Again, since base angles are equal, 2 = ______. 105
75
75
105
105 2
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6.5 Trapezoids and Kites

16. Your Turn
CDEF is an isosceles trapezoid with CE = 10 and E = 95. Find DF, C, D and F. E ?
95
95
85 ?
85 ?
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6.5 Trapezoids and Kites

17. Name the vertices of CDEF.
C must be where?
Now label the rest.
CE is a diagonal and is 10.
DF = ____. (In an isosc. trap., diags are .) 10 E D
95
95
85
85 F C
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6.5 Trapezoids and Kites

18. Triangle Review
The midsegment of a triangle connects the midpoints of two sides.
The midsegment is parallel to the third side and one-half its length.
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6.5 Trapezoids and Kites

19. Trapezoid Midsegment Connects the midpoints of the legs.
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6.5 Trapezoids and Kites

20. Midsegment Theorem
The midsegment of a trapezoid is parallel to each base and its length is one-half the sum of the bases. A B C D E F
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6.5 Trapezoids and Kites

21. Example AB = 24 and DC = 30. Find EF. 24 B A E F D C 30
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6.5 Trapezoids and Kites

22. Your Turn ? AB = 10 and EF = 15. Find CD. 10 B A 15 E F D C
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6.5 Trapezoids and Kites

23. Solution ? 20 10 B A 15 E F D C December 8, 2018
6.5 Trapezoids and Kites

24. Trapezoid Summary A trapezoid has 2 parallel sides.
A trapezoid is NOT a parallelogram.
The legs of an isosceles trapezoid are congruent.
The base angles of an isosceles trapezoid are congruent.
The midsegment of a trapezoid is one-half the sum of the two bases.
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6.5 Trapezoids and Kites

25. Kites
A kite is a quadrilateral with two pairs of congruent sides, but opposite sides are not congruent. (They’re not parallel, either.)
These are congruent consecutive sides.
And these are congruent consecutive sides.
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6.5 Trapezoids and Kites

26. Kites
A kite is a quadrilateral with two pairs of congruent sides, but opposite sides are not parallel.
There are NO parallel sides.
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6.5 Trapezoids and Kites

27. Kite Properties
The diagonals of a Kite are perpendicular. (Theorem 6.18)
One pair of opposite angles is congruent. (Theorem 6.19)
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6.5 Trapezoids and Kites

28. Problem GHJK is a kite. Find GH. H J G 5 2 K December 8, 2018
6.5 Trapezoids and Kites

29. Solution 52 + 22 = GK2 29= GK2 Use Pythagorean Theorem. H J G 5 2 K
Segments GK and GH are congruent. H J G 5 2 K
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6.5 Trapezoids and Kites

30. Another Kite Problem RSTU is a kite. Find R, S, T. S x + 30 R T x
125 U
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6.5 Trapezoids and Kites

31. Solution ? 40 70 The sum of the angles in a quadrilateral is 360.
125 R
x + 30 T
40 x
70
125 U
The sum of the angles in a quadrilateral is 360.
x x = 360
2x = 360
2x = 80
x = 40
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6.5 Trapezoids and Kites

32. Questions?
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6.5 Trapezoids and Kites

33. True or False? In ABCD, diagonals AC and BD are perpendicular.
ABCD is a kite.
True or False?
FALSE.
Why?
The diagonals of a rhombus are also perpendicular.
December 8, 2018
6.5 Trapezoids and Kites