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Trapezoids and Kites
Additional Properties
Trapezoid
General Definition
one set of parallel sides
base1
leg
leg
base2
Types of Trapezoids
Scalene or basic trap – previous page
Right Trap – has two right angles on same leg
base1
leg
leg
base2
Isosceles Trap – both legs are congruent
base1
leg
leg
base2
Diagonals of an Isosceles Trapezoid
Can you prove the diagonals congruent
Given: Isosceles Trapezoid
Prove: AC=BD
B
A
C
D
Examples Trap
Kite
Two pairs of consecutive sides congruent
Kite Properties
Given: Kite
Prove: <A=<C
B
C
A
Angles formed by non congruent sides are
congruent
D
Kite Properties
Given: Kite
Prove: <ADB=<CDB and
<ABD=<CBD (segment BD is
an angle bisector)
Diagonal connecting non congruent angles bisects
Those angles
B
C
A
D
Kite Properties
Given: Kite
Prove: AE=CE
Diagonal connecting the congruent angles is bisected
by the other diagonal
B
A
C
E
D
Kite Properties
The two diagonals of a kite are perpendicular
How would you prove this?
Pythagorean Theroem
Examples Kites
Summary
Trapezoid – 1 pair of parallel sides
Right Trapezoid – 1 pair of parallel sides, with 1 leg perpendicular to
both sides
Isosceles Trapezoid – 1 pair of parallel sides and both legs are
congruent
- diagonals are congruent
Kite – 2 pairs of consecutive sides congruent
- angles formed by non congruent sides are congruent
- diagonals are perpendicular
- diagonal connecting non congruent angles is an angle
bisector
- diagonal connecting congruent angles is bisected by other
diagonal
Homework
Pg 271 1-8 Honors 9 and 10