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Trapezoids and Kites
Objective: Students will be able to
apply additional properties to prove
shapes are triangles and kites.
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