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Lesson 5.3 Trapezoids and Kites. Homework: 5.3/1-8,19 QUIZ Wednesday 5.1 – 5.4. PROCEDURES for today:. 1. OPEN TEXTBOOKS 2. Tools – patty paper(2), protractor, ruler 3. INVESTIGATIONs 1 & 2 – ALL steps 4. Complete the 4 kite conjectures & the 3 trapezoid conjectures. Definition. - PowerPoint PPT Presentation
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Lesson 5.3Trapezoids and Kites
Homework: 5.3/1-8,19
QUIZ Wednesday 5.1 – 5.4
1. OPEN TEXTBOOKS2. Tools – patty paper(2), protractor, ruler3. INVESTIGATIONs 1 & 2 – ALL steps4. Complete the 4 kite conjectures & the 3 trapezoid conjectures
PROCEDURES for today:
DefinitionKite – a quadrilateral that has two pairs of
consecutive congruent sides, but opposite sides are not congruent.
Perpendicular Diagonals of a Kite
If a quadrilateral is a kite, then its diagonals are perpendicular.
D
C
A
B
BDAC
Non-Vertex Angles of a Kite
If a quadrilateral is a kite, then non-vertex angles are congruent
D
C
A
B
A C, B D
Vertex diagonals bisect vertex angles
D
C
A
B
If a quadrilateral is a kite then the vertex diagonal bisects the vertex angles.
Vertex diagonal bisects the non-vertex diagonal
D
C
A
B
If a quadrilateral is a kite then the vertex diagonal bisects the non-vertex diagonal
Definition-a quadrilateral with exactly one pair of parallel sides.
Leg Leg Leg Leg
BaseBase
BaseBaseAA BB
CC DD››
››
Trapezoid
<A + <C = 180<A + <C = 180
<B + <D = 180<B + <D = 180
AA BB
CC DD››
››
Leg Angles are Supplementary
Property of a Trapezoid
Isosceles Trapezoid
Definition - A trapezoid with congruent legs.
Isosceles Trapezoid - Properties
| | ||
1) Base Angles Are Congruent2) Diagonals Are Congruent
Example
PQRS is an isosceles trapezoid. Find m P, m Q and mR.
50S R
P Q
m R = 50 since base angles are congruent
mP = 130 and mQ = 130 (consecutive angles of parallel lines cut by a transversal are )
Find the measures of the angles in trapezoid
48
m< A = 132m< B = 132m< D = 48
Find BE
AC = 17.5, AE = 9.6
E
Example
Find the side lengths of the kite.
20
12
1212
UW
Z
Y
X
Example Continued
WX = 4 34
likewise WZ = 4 34
XY =12 2
likewise ZY =12 2
20
12
1212
UW
Z
Y
X
We can use the Pythagorean Theorem to find the side lengths.
122 + 202 = (WX)2
144 + 400 = (WX)2
544 = (WX)2
122 + 122 = (XY)2
144 + 144 = (XY)2
288 = (XY)2
Find the lengths of the sides of the kite
W
X
Y
Z
4
55
8
Find the lengths of the sides of kite to the nearest tenth
4
2
2
7
Example 3Find mG and mJ.
60132
J
G
H K
Since GHJK is a kite G J
So 2(mG) + 132 + 60 = 360
2(mG) =168
mG = 84 and mJ = 84
Try This!
RSTU is a kite. Find mR, mS and mT.
x
125
x+30
S
U
R T
x +30 + 125 + 125 + x = 360
2x + 280 = 360
2x = 80
x = 40
So mR = 70, mT = 40 and mS = 125
Try These
base
base
legleg
A B
D C base
base
legleg
A B
D C
1. If <A = 134, find m<D2. m<C = x +12 and m<B = 3x – 2, find x and the measures of the 2 angles
m<D = 46
x = 42.5m<C = 54.5m<B = 125.5
Using Properties of Trapezoids
Find the area of this trapezoid.
When working with a trapezoid, the height may be measured anywhere between the two bases. Also, beware of "extra" information. The 35 and 28 are not needed to compute this area.
Area of trapezoid = 212
1bbh
A = ½ * 26 * (20 + 42)
A = 806
Using Properties of Trapezoids
Find the area of a trapezoid with bases of 10 in and 14 in, and a height of 5 in.
Example 2
Using Properties of Kites
D
A
B
C
Area Kite = one-half product of diagonals
212
1ddA
BDACArea 2
1
Using Properties of Kites
D
A
B
C
Example 6
E
24 4
4
ABCD is a Kite.
a) Find the lengths of all the sides.
b) Find the area of the Kite.
Venn Diagram:
http://teachers2.wcs.edu/high/rhs/staceyh/Geometry/Chapter%206%20Notes.ppt#435,22,6.2 – Properties of Parallelograms
Flow Chart:
Homework