1 12/6/12 unit 3 polygons and circles trapezoids and kites
TRANSCRIPT
![Page 1: 1 12/6/12 Unit 3 Polygons and Circles Trapezoids and Kites](https://reader036.vdocuments.site/reader036/viewer/2022070403/56649f2c5503460f94c46fa7/html5/thumbnails/1.jpg)
1
12/6/12 Unit 3 Polygons and Circles
Trapezoids
and Kites
![Page 2: 1 12/6/12 Unit 3 Polygons and Circles Trapezoids and Kites](https://reader036.vdocuments.site/reader036/viewer/2022070403/56649f2c5503460f94c46fa7/html5/thumbnails/2.jpg)
2
IsoscelesTrapezoid
Quadrilaterals
Rectangle
Parallelogram
Rhombus
Square
Flow Chart
Trapezoid
Non Parallelograms
Kite
![Page 3: 1 12/6/12 Unit 3 Polygons and Circles Trapezoids and Kites](https://reader036.vdocuments.site/reader036/viewer/2022070403/56649f2c5503460f94c46fa7/html5/thumbnails/3.jpg)
3
TrapezoidA quadrilateral with exactly one pair of parallel sides.Definition:
BaseLeg
An Isosceles trapezoid is a trapezoid with congruent legs.
Trapezoid
The parallel sides are called bases and the non-parallel sides are called legs.
Isosceles trapezoid
![Page 4: 1 12/6/12 Unit 3 Polygons and Circles Trapezoids and Kites](https://reader036.vdocuments.site/reader036/viewer/2022070403/56649f2c5503460f94c46fa7/html5/thumbnails/4.jpg)
A Trapezoid is a quadrilateral with exactly one pair of parallel sides.
Trapezoid Terminology • The parallel sides are called BASES. • The nonparallel sides are called LEGS. • There are two pairs of base angles, the two touching the top base, and the two touching the bottom base.
![Page 5: 1 12/6/12 Unit 3 Polygons and Circles Trapezoids and Kites](https://reader036.vdocuments.site/reader036/viewer/2022070403/56649f2c5503460f94c46fa7/html5/thumbnails/5.jpg)
5
Properties of Isosceles Trapezoid
A B and D C
2. The diagonals of an isosceles trapezoid are congruent.
1. Both pairs of base angles of an isosceles trapezoid are congruent.
A B
CD
Base Angles
AC DB
![Page 6: 1 12/6/12 Unit 3 Polygons and Circles Trapezoids and Kites](https://reader036.vdocuments.site/reader036/viewer/2022070403/56649f2c5503460f94c46fa7/html5/thumbnails/6.jpg)
ISOSCELES TRAPEZOID - If the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid.
**** - Both pairs of base angles of an isosceles trapezoid are congruent.
**** - The diagonals of an isosceles trapezoid are congruent.
**** – If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.
![Page 7: 1 12/6/12 Unit 3 Polygons and Circles Trapezoids and Kites](https://reader036.vdocuments.site/reader036/viewer/2022070403/56649f2c5503460f94c46fa7/html5/thumbnails/7.jpg)
Example 1
CDEF is an isosceles trapezoid with leg CD = 10 and mE = 95°. Find EF, mC, mD, and mF.
![Page 8: 1 12/6/12 Unit 3 Polygons and Circles Trapezoids and Kites](https://reader036.vdocuments.site/reader036/viewer/2022070403/56649f2c5503460f94c46fa7/html5/thumbnails/8.jpg)
10
The median of a trapezoid is the segment that joins the midpoints of the legs.
The median of a trapezoid is parallel to the bases, and its measure is one-half the sum of the measures of the bases.
Median
1b
2b
1 2
1( )
2median b b
Median of a Trapezoid
![Page 9: 1 12/6/12 Unit 3 Polygons and Circles Trapezoids and Kites](https://reader036.vdocuments.site/reader036/viewer/2022070403/56649f2c5503460f94c46fa7/html5/thumbnails/9.jpg)
Example 3
102°
65°
17 in
24 in.
A B
CD
E F
Find AB, mA, and mC
![Page 10: 1 12/6/12 Unit 3 Polygons and Circles Trapezoids and Kites](https://reader036.vdocuments.site/reader036/viewer/2022070403/56649f2c5503460f94c46fa7/html5/thumbnails/10.jpg)
Example 4
![Page 11: 1 12/6/12 Unit 3 Polygons and Circles Trapezoids and Kites](https://reader036.vdocuments.site/reader036/viewer/2022070403/56649f2c5503460f94c46fa7/html5/thumbnails/11.jpg)
A quadrilateral is a kite if and only if it has two distinct pair of consecutive sides congruent.
• The vertices shared by the congruent sides are ends. • The line containing the ends of a kite is a symmetry line for a kite. • The symmetry line for a kite bisects the angles at the ends of the kite. • The symmetry diagonal of a kite is a perpendicular bisector of the other diagonal.
![Page 12: 1 12/6/12 Unit 3 Polygons and Circles Trapezoids and Kites](https://reader036.vdocuments.site/reader036/viewer/2022070403/56649f2c5503460f94c46fa7/html5/thumbnails/12.jpg)
![Page 13: 1 12/6/12 Unit 3 Polygons and Circles Trapezoids and Kites](https://reader036.vdocuments.site/reader036/viewer/2022070403/56649f2c5503460f94c46fa7/html5/thumbnails/13.jpg)
Using Properties of Kites
A
B C
D
If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.
mB = mC
![Page 14: 1 12/6/12 Unit 3 Polygons and Circles Trapezoids and Kites](https://reader036.vdocuments.site/reader036/viewer/2022070403/56649f2c5503460f94c46fa7/html5/thumbnails/14.jpg)
Using Properties of Kites
D
A
B
C
Example 6
E
2
4 4
4
ABCD is a Kite.
a) Find the lengths of all the sides.
b) Find the area of the Kite.
![Page 15: 1 12/6/12 Unit 3 Polygons and Circles Trapezoids and Kites](https://reader036.vdocuments.site/reader036/viewer/2022070403/56649f2c5503460f94c46fa7/html5/thumbnails/15.jpg)
Using Properties of Kites
29
Example 7
CBDE is a Kite. Find AC.
5B
C
D
EA
![Page 16: 1 12/6/12 Unit 3 Polygons and Circles Trapezoids and Kites](https://reader036.vdocuments.site/reader036/viewer/2022070403/56649f2c5503460f94c46fa7/html5/thumbnails/16.jpg)
Using Properties of Kites
x°
125°
(x + 30)°
A
B C
D
Example 8
ABCD is a kite. Find the mA, mC, mD