Transcript Use Properties of Trapezoids and Kites
Use Properties of Trapezoids and Kites
Chapter 8.5
Trapezoids
Trapezoids are quadrilaterals that have 2 parallel sides The parallel sides are called the bases.
◦ A trapezoid has 1 pair of base angles.
The non-parallel sides are called the legs.
base Leg Leg base
Is it a trapezoid?
Are the bases parallel?
Find the slope of each base.
If the slopes are the same, then it is a trapezoid.
Isosceles Trapezoids
Isosceles triangles have 2 congruent sides with 2 pairs of congruent angles.
The diagonals of an isosceles trapezoid are also congruent.
If it is Isosceles find the missing angles.
It is isosceles!
127º 127º 53º Because it is an isosceles trapezoid, the base angles are congruent.
Therefore m < A = m < B, and m < D = m < C Angle A and Angle D are supplementary.
180 – 53 = 127
Find the missing angles if it is an Isosceles Trapezoid.
83º 97º 83º
Midsegments
A midsegment is a segment that connects 2 midpoints.
The midsegment of a trapezoid connects the midpoints of the legs.
Find the length of the midsegment
HK
1 2 (
DE
GF
)
HK
1 2 ( 6 18 )
HK
12
Things always have to be more difficult
migsegment
1 2 (
base
1
base
2 ) 19.5
5x + 3 19 .
5 1 2 ( 27 5
x
3 ) 19 .
5 19 .
5 4 .
5 1 2 15 ( 30 2 .
5
x
5
x
) 2 .
5
x
1 .
8
x
Find x
45 52.5
10x + 15
migsegment
1 2 (
base
1
base
2 ) 52 .
5 1 2 ( 45 10
x
15 ) 52 .
5 52 .
5 22 .
5 1 2 ( 60 30 5
x
10
x
) 5
x
4 .
5
x
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Kites
A kite is a quadrilateral with 2 pairs of congruent sides, but the opposite sides are not congruent.
3
Diagonals
3 2 9 18 3 2 9
XY XY
2
XY
2 2 18
XY
2 2
XY
WX a
If the diagonals of a kite are perpendicular, then what shape is created by the diagonals?
If we are given these side lengths, can we find the missing sides XY, WX, YZ , and WZ?
2 3 2 9
b
2 5 2 25
c YZ
2 34
XY
2 2 2 34 34
XY
2
YZ
WZ
Find XY, ZY, WX, and WZ
2√13 6√5
6 2 12 2
XY
2 36 144
XY
2 6 180 180
XY
2
XY
2 5
XY
ZY
4 16 2 52 6 2 36
WX WX
2
WX
2 2 52
WX
2 2 13
WX
WZ
Find XY, YZ, WZ, and WX
10 2 5 2
XY
2
5√5 √461
10 2 19 2
WZ
2 100 361
WZ
2 461
WZ
2 461
WZ
2 461
WZ
WX
100 25
XY
2 5 125 125
XY
2
XY
2 5
XY
YZ
The figure below is a kite, find the missing angles What is the sum of the interior angles of a kite?
360 100 + 40 + m ó E + m ó G = 360 140 + m ó E + m ó G = 360 m ó E + m ó G = 220 What do we know about the measures of the angles E and G?
They are congruent!
220 110 2
Find the missing angles
What do we know about the measures of the angles F and H?
They are congruent!
110º
60 + 110 + 110 + m ó G = 360
80º
280 + m ó G = 360 m ó G = 80
Find the missing angles
150 + 90 + m ó F + m ó G = 360 240 + m ó F + m ó G = 360 m ó F + m ó G = 120 m ó F = m ó G 120 60 2