Properties of Kites/Trapezoids

Section6.6

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

Kites up close

The longer diagonal is thePerpendicular bisector of theShorter diagonal

The diagonals create 2 pairsOf congruent right triangles

There are also twoIsosceles Triangles

Created

Find the value of x,y,z in the Kite

6

Given JK = 28cm

J

K

8

X

YZ

First Find ZSince JK = 28Z must be 20

20

Then use the Pythagorean

Theorem to find X

A2+B2=C2

62+82=X2

36+64=100

SO 10 = X

=10

6

8

10

20

Now find y62+202= y2

36 + 400 =436

So 28.88= y

Y=28.9

Trapezoids

Only 1 pair ofSides are parallel

base

base

side

side

Find the value of C16cm

18cm

26cm

60

c

If we imagine a dashedLine we create a special

30-60-90 triangle

10

So C = 20

Isosceles TrapezoidBases are parallel

AndTwo sides

are congruent

Base angles are congruent

Supplementary

angles

Find the missing angles

74

x y

z

These are congruent

These areSupp.

X = 180 – 74= 106

106

74

106

Challenge: find all variables

42

73

23

xy

z84

Z=96

Y=73

23

X=42

42

First place anyOther angles

Since each Triangle

Totals 180

Z and 84Make a

Straight line

Workbook page 42

Do problems 1-12