1. 6-6 Trapezoids & Kites
The student will be able to:
Recognize and apply the properties of trapezoids.
Recognize and apply the properties of kites.

2. Trapezoids
Trapezoid – a quadrilateral with exactly one pair of parallel sides.
The parallel sides are called bases.
The nonparallel sides are called legs.
If the legs of a trapezoid are congruent, then it is an isosceles trapezoid.
An isosceles trapezoid has the following properties:
The legs are congruent.
Each pair of base angles is congruent.
The diagonals are congruent.

3. What do we know about base angles of an isosceles trapezoid?
Example 1: The speaker shown is an isosceles trapezoid. If inches, and inches, find each measure. a. 8
What do we know about base angles of an
isosceles trapezoid? 19
The base angles are congruent, so 85 85
What do we know about consecutive interior angles?
They are supplementary.
85 + x = 180
-85
x = 95

4. Example 1: The speaker shown is an isosceles trapezoid
Example 1: The speaker shown is an isosceles trapezoid. If inches, and inches, find each measure. b.
What do we know about diagonals of an
isosceles trapezoid?
The diagonals are congruent, so and
8 + x = 19
- 8
x = 11

5. Midsegment of a trapezoid: The segment that joins midpoints of the legs of a trapezoid.
The midsegment has the following properties:
it is parallel to each base
it bisects each leg
its measure is ½ the sum of the
lengths of the bases
= ½( )

6. Example 2:
In the figure, is the midsegment of trapezoid FGJK. What is the value of x?
= ½( )
30 = ½( 20 + x)
30 = 10 + ½x
-10
20 = ½x
40 = x

7. Trapezoid ABCD is shown below. If
is parallel to What is the x-coordinate
of point G?
Point G is the midpoint of so use the
midpoint formula to find G.
m = (10.5 , 2)
Are we through?
No.
The x-coordinate of G is 10.5.

8. Kite – a quadrilateral with exactly 2 pairs of consecutive congruent sides.
A kite has the following properties:
Diagonals are perpendicular.
One pair of opposite angles is congruent. It’s always the angle between two sides that aren’t congruent.

9. What do we know about angles of a kite?
Example 4:
If WXYZ is a kite, find
What do we know about angles of a kite?
121
The angles between the two non-congruent sides are =.
What is the sum of the interior angles of a kite?
360
x = 360
315 + x = 360
-315
x = 45

10. Example 5:
If MNPQ is a kite, find
What do we know about angles formed by the diagonals of a kite?
They are right angles.
What do we use to find the lengths of the segments of right triangles?
The Pythagorean Theorem
a2 + b2 = c2
= c2
= c2
100 = c2
10 = c

11. Example 5:
The vertices of ABCD are A(-3, -1), B(-1,3)
C(2, 3), and D(4, -1). Verify that ABCD is
a trapezoid. Is it an isosceles trapezoid?
What will tell us it’s a trapezoid?
What will tell us it’s a trapezoid?
1 pair of parallel bases
What will tell us it’s an isosceles trapezoid?
Congruent legs
What formulas can we use to find if the bases are parallel & legs congruent?
Slope 4 times and distance formula for only the legs.

12. The vertices of ABCD are A(-3, -1), B(-1,3)
C(2, 3), and D(4, -1). Verify that ABCD is
a trapezoid. Is it an isosceles trapezoid?
Is it a trapezoid?
yes
Is it an isosceles trapezoid?
Yes. There are exactly 1 pair of parallel
lines and the legs are congruent.