Properties of Kites/Trapezoids

1
Properties of Kites/Trapezoids

• Section6.6

2
These are not P-grams

• In parallelograms, all opposite sides are
  parallel
• In kites and trapezoids this is not true
• In kites, no sides are parallel
• In trapezoids only 1 pair of sides are parallel

3
Kites up close
There are also two Isosceles Triangles Created
The longer diagonal is the Perpendicular bisector
of the Shorter diagonal
The diagonals create 2 pairs Of congruent right
triangles
4
Find the value of x,y,z in the Kite
Given JK 28cm
10
K
X
Then use the Pythagorean Theorem to find X
6
8
A2B2C2 6282X2 3664 100 SO 10 X
20
Y
Z
First Find Z Since JK 28 Z must be 20
J
5
Now find y 62202 y2 36 400 436 So 28.88 y
10
8
6
Y28.9
20
6
Trapezoids
Only 1 pair of Sides are parallel
base
side
side
base
7
Find the value of C
16cm
So C 20
c
18cm
60
10
26cm
If we imagine a dashed Line we create a
special 30-60-90 triangle
8
Isosceles Trapezoid
Bases are parallel And Two sides are congruent
Supplementary angles
Base angles are congruent
9
Find the missing angles
X 180 74 106
x
y
These are Supp.
106
106
74
z
74
These are congruent
10
Challenge find all variables
First place any Other angles
X42
x
y
73
Y73
84
z
Since each Triangle Totals 180
Z96
23
23
42
42
Z and 84 Make a Straight line
11
Workbook page 42

• Do problems 1-12