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!
53º
127º
127º
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
1
HK  ( DE  GF )
2
1
HK  (6  18)
2
HK  12
Things always have to be more
difficult
1
migsegment 
19.5
5x + 3
2
(base1  base 2 )
1
19 .5  (27  5 x  3)
2
1
19 .5  (30  5 x)
2
19.5  15  2.5 x
4 .5  2 .5 x
1 .8  x
Find x
45
52.5
10x + 15
1
migsegment  (base1  base 2 )
2
1
52.5  (45  10 x  15)
2
1
52.5  (60  10 x)
2
52.5  30  5 x
22.5  5 x
4 .5  x
Page 546, #3 – 15, 25 - 27
Kites

A kite is a quadrilateral with 2 pairs of
congruent sides, but the opposite sides
are not congruent.
Diagonals
3  3  XY
2
9  9  XY
2
18  XY
2
2
18  XY
2
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?
3  5  YZ
2
2
22
a 9 b25 cXY
2
34  XY
2
3 2  XY  WX
2
2
34  XY
2
2
34  YZ  WZ
Find XY, ZY, WX, and WZ
2√13
6√5
6  12  XY
2
2
2
36  144  XY 2
180  XY 2
2
180  XY
6 5  XY  ZY
42  62  WX 2
16  36  WX 2
52  WX 2
2
52  WX
2 13  WX  WZ
Find XY, YZ, WZ, and WX
102  52  XY 2
5√5
100 25  XY
2
125  XY
125  XY 2
2
√461
10  19  WZ
2
100 361 WZ
2
2
2
461 WZ
461  WZ 2
2
461  WZ  WX
5 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 + mó E + mó G = 360
140 + mó E + mó G = 360
mó E + mó 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 + mó G = 360
80º
280 + mó G = 360
mó G = 80
Find the missing angles
150 + 90 + mó F + mó G = 360
240 + mó F + mó G = 360
mó F + mó G = 120
mó F = mó G
120
 60
2