Use properties of kites and trapezoids to solve problems

1. Obj. 28 Kites & Trapezoids
The student is able to (I can):
• Use properties of kites and trapezoids to solve problems

2. kite
A quadrilateral with exactly two pairs of
congruent consecutive nonparallel sides.
Note: In order for a quadrilateral to be a
kite, no sides can be parallel and opposite
sides cannot be congruent.

3. If a quadrilateral is a kite, then its
diagonals are perpendicular.
If a quadrilateral is a kite, then exactly one
pair of opposite angles is congruent.

4. Example
In kite NAVY, m∠YNA=54º and
m∠VYX=52º. Find each measure.
1. m∠NVY
90 — 52 = 38º
2. m∠XYN
180 − 54 126
=
= 63°
2
2
3. m∠NAV
63 + 52 = 115º
N
A
V
X
Y

5. trapezoid
A quadrilateral with exactly one pair of
parallel sides. The parallel sides are called
bases and the nonparallel sides are the
legs.
legs Angles along one leg are
supplementary.
base angles
>
base
leg
leg
base
>
base angles
Note: a trapezoid whose legs are
congruent is called an isosceles trapezoid
trapezoid.

6. Isosceles Trapezoid Theorems
If a quadrilateral is an isosceles trapezoid,
then each pair of base angles is congruent.
If a trapezoid has one pair of congruent
base angles, then the trapezoid is
isosceles.
A trapezoid is isosceles if and only if its
diagonals are congruent.
R
>
A
∠R ≅ ∠A, ∠T ≅ ∠P
TR ≅ AP
TA ≅ RP
T
>
P

7. Examples
1. Find the value of x.
5x = 40
x=8
5xº
40º
140º
2. If NS=14 and BA=25, find SE.
SE = 25 — 14 = 11
B
E
S
N
A

8. Trapezoid Midsegment Theorem
The midsegment of a trapezoid is parallel
to each base, and its length is one half
the sum of the lengths of the bases.
H
F
>
A
V
Y
>
R
AV HF, AV YR
1
AV = (HF + YR )
2

9. Examples
MY is the midsegment of trapezoid OFIG.
1. If OF=22 and GI=30, find MY.
1
MY = ( 22 + 30 ) = 26
2
2. If OF=16 and MY=18, find GI.
1
18 = ( 16 + GI )
2
36 = 16 + GI
GI = 20
O
F
>
Y
M
G
>
I