This document discusses properties of trapezoids and kites. It defines trapezoids as quadrilaterals with one set of parallel sides and defines properties such as the relationship between base angles and legs. It also discusses finding the median and using heights to find base lengths. Kites are defined as quadrilaterals with two sets of consecutive congruent sides and perpendicular diagonals, with only one pair of opposite angles being congruent. Examples are given of finding missing angle and side measures of kites using their properties.

1. Section 6-6
Spi.3.2.H
Jim Smith JCHS

2. Trapezoids are quadrilaterals
with exactly 1 pair of parallel sides
Leg Leg
Base
Base
A B
C D
Base Angles
A + C = 180
B + D = 180
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3. Isosceles Trapezoids Have
Congruent Legs
1) Base Angles Are Congruent
2) Diagonals Are Congruent

4. The Endpoints Of The Median
Of A Trapezoid Are The Midpoints
Of The Legs
Median

5. Median
Median = ½ ( b1 + b2 ) or
2 Median = ( b1 + b2 ) or
The Median Is The Average
Of The 2 Bases
b1
b2

6. 6
24
X
2X = 6 + 24
2X = 30
X = 15
X + 2
X + 20
4X + 32
2 ( X + 20 ) = X + 2 + 4X + 32
2X + 40 = 5X + 34
40 = 3X + 34
6 = 3X
2 = X
median

7. Sometimes it’s helpful
to know that 2 heights
of a trapezoid form
a rectangle. This can
help us find the length
of a base.
If it’s an isosceles trapezoid, the
triangles will also be congruent.

8. Kites
Kites are quadrilaterals
with exactly 2 pairs of
consecutive congruent sides
Opposite sides are NOT
parallel or congruent.

9. Diagonals of a kite
are perpendicular.
Only one pair of opposite
angles in a kite are congruent

10. Can you find
Congruent triangles?
What method did you use?
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11. If GHJK is a kite, find each measure.
1. Find m∠JRK.
2. If m∠GHJ = 90, find m∠HGJ.
3. If HJ = 7, find HG.
4. If GR = 5, find RJ.
5. If m∠GHJ = 96 and m∠GKJ = 52, find m∠HGK.
G
H
J
K
R
1. 90°
2. 45°
3. 7
4. 5
5. 106°