Download Trapezoids and Kites

Entry Task

What is the sum of the interior angles of a
dodecagon?

What is the measure of one exterior angle
of a regular dodecagon?
A
Solve for the
measure of
∠𝐸 𝑎𝑛𝑑 ∠𝐷
𝑥
E
2𝑥 − 50
𝑥+6
D
𝑥 − 20
𝑥+4
C
B
Warm Up
180(5 − 2)
𝑇𝑜𝑡𝑎𝑙 𝐼𝑛𝑡𝑒𝑟𝑖𝑜𝑟 𝐷𝑒𝑔𝑟𝑒𝑒𝑠: 540°
180(𝑛
𝒙 + 𝑥 − 20 + 𝒙 + 𝟒 + 𝑥 + 6 + 𝟐𝒙 − 𝟓𝟎 = 540
Solve for the
measure of
∠𝐸 𝑎𝑛𝑑 ∠𝐷
𝟔𝒙 − 𝟔𝟎 = 540
𝟔𝒙 = 600
𝒙 = 100
A
𝑥
E
∠𝑬 = 𝟏𝟓𝟎°
∠𝑫 = 𝟏𝟎𝟔°
2𝑥 − 50
𝑥+6
D
𝑥 − 20
𝑥+4
C
B
Homework Questions
5.3
Trapezoids and Kites
Definition

Kite – a quadrilateral that has two pairs
of consecutive congruent sides, but
opposite sides are not congruent.
Parts of a Kite
Vertex angles:
<B & <D
C
B
Non-Vertex
angles: <A & <C
Vertex diagonal
BD
D
A
Non-Vertex diagonal
CA
Kite Angles Theorem

non-vertex angles are congruent
C
D
B
A
A  C, B  D

Kite Diagonal Theorem
◦ Diagonals are perpendicular to each other
C
B

Kite Diagonal Bisector
Theorem
A
◦ Vertex Angle’s diagonal is the
perpendicular bisector of the other
D
AC  BD
Kite Angle Bisector Theorem
Vertex Angles are bisected
C
B
D
A
Trapezoid
Definition-a quadrilateral with exactly
one pair of parallel sides.
A
Base
› B
Leg
Leg
C
›
Base
D
Trapezoid Investigation
Draw two parallel lines, labeled l1 and l2. These
will be the two bases of your trapezoid.
 Draw the two legs of your trapezoid; these legs
can extend on forever just like a transversal
 Label your angles A, B, C, and D
 Using what you know about parallel lines, what
can you say about these angles?

PropertyConsecutive
of a Trapezoid
Trapezoid
“CoInterior” Angle Theorem
A  C  180
B  D  180
o
A
›
B
o
C
›
D
Isosceles Trapezoid
A trapezoid with congruent legs
Isosceles Trapezoid - Properties
1) Base Angles Are Congruent
2) Diagonals Are Congruent
Prove: Diagonals Are Congruent
Homework
Pg. 271 #1-10, 19
 Quiz 5.1-5.4 Friday
