This lesson covers properties of trapezoids and kites. It defines a trapezoid as a quadrilateral with one pair of parallel sides, and defines properties including that the nonparallel sides are legs and the parallel sides are bases. An isosceles trapezoid has congruent legs. The lesson also defines a kite as a quadrilateral with two pairs of consecutive congruent sides, and defines properties such as perpendicular diagonals and congruent non-vertex angles. Examples of solving problems involving finding angle measures of trapezoids and kites are provided.

1. Trapezoid and Kite
Lesson 2

2. Lesson 2
• proves theorems on trapezoids and kites.
• Solve problems involving kite and trapezoid

3. Lesson 2
SLIDE
•Parallelogram
•Rectangle
•Square
•Rhombus
•Trapezoid
•Trapezium
•Isosceles Trapezoid
•Kite

4. Lesson 2
• A trapezoid is a quadrilateral with exactly one pair of parallel
sides.
• The parallel sides are called bases.
• The nonparallel sides are called legs.
• At each side of a base there is a pair of base angles.
A
D C
B
leg leg
base
base

5. Lesson 2

6. • Isosceles trapezoid: A trapezoid with congruent legs.
• Both pairs of base angles of an isosceles trapezoid are
congruent.
• The diagonals of an isosceles trapezoid are congruent.
A
D C
B
 A   B,  C   D
A
D C
B
BD
AC
if
only
and
if
isosceles
is
ABCD 

7. Lesson 2
• PQRS is an isosceles trapezoid.
• Find m P, m Q and mR.
50
S R
P Q
m R = 50 since base angles are congruent
mP = 130 and mQ = 130 (consecutive angles
of parallel lines cut by a transversal are )

8. Lesson 2
• Find mA, mB, mD.

9. Lesson 2
The median of a trapezoid is
parallel to the bases, and its
measure is one-half the sum of
the measures of its bases.
The median of a trapezoid is the segment that joints the
midpoints of the legs (PQ).
midsegment N
M
A D
B C
BC)
AD
2
1
MN
,
BC
ll
MN
AD
ll
MN (
, 


10. Lesson 2
For trapezoid ABCD, F and G
Are midpoints of the legs. Find FG.
DC)
AB
2
1
FG ( 


11. Lesson 2
Find FG.
DC)
AB
2
1
FG ( 


12. Lesson 2
A
C D
B
Area of a trapezoid: If a trapezoid has
an area of A square units, bases of b1
and b2 units and height of h units, then
A = ½(b1 + b2 )h.
h

13. Trapezoid:
• One pair of parallel sides.
• Consecutive angles between the bases are
supplementary.
• Midsegment is the average of the two bases.
Properties of Trapezoids
>
>
b1
b2
m

14. Trapezoid:
• One pair of parallel sides.
• Consecutive angles between the bases are
supplementary.
• Midsegment is the average of the two bases.
Properties of Trapezoids
>
>
b1
b2
m

15. Isosceles Trapezoid:
• One pair of parallel sides.
• Trapezoid whose non-parallel sides are congruent.
• Base angles are congruent.
• Diagonals are congruent.
Properties of Trapezoids
>
>

16. Isosceles Trapezoid:
• One pair of parallel sides.
• Trapezoid whose non-parallel sides are congruent.
• Base angles are congruent.
• Diagonals are congruent.
Properties of Trapezoids

17. Lesson 2
Kite – a quadrilateral that has two pairs of consecutive congruent sides,
but opposite sides are not congruent.

18. Lesson 2
• If a quadrilateral is a kite, then its diagonals are perpendicular.
D
C
A
B
BD
AC 

19. Lesson 2
• If a quadrilateral is a kite, then exactly one pair of opposite angles are
congruent
D
C
A
B
A  C, B  D

20. Lesson 2
• Find mG and mJ.
60
132
J
G
H
K
Since GHJK is a kite G  J
So 2(mG) + 132 + 60 = 360
2(mG) =168
mG = 84 and mJ = 84

21. Lesson 2
In kite WXYZ, mWXY = 104°, and
mVYZ = 49°. Find each measure.
1. mVZY
2. mVXW
3. mXWZ
W
X
Y
Z
V

22. Lesson 2
• RSTU is a kite. Find mR, mS and mT.
x
125
x+30
S
U
R T
x +30 + 125 + 125 + x = 360
2x + 280 = 360
2x = 80
x = 40
So mR = 70, mT = 40 and mS = 125
125

23. Properties of a Kite
Kite:
• 2 distinct pairs of consecutive congruent sides.
• One diagonal is the  bisector of the other.
• Non-vertex angles are congruent.
• One diagonal bisects both vertex angles.
Vertex Angles
Non-vertex Angles

24. Properties of a Kite
Kite:
• 2 distinct pairs of consecutive congruent sides.
• One diagonal is the  bisector of the other.
• Non-vertex angles are congruent.
• One diagonal bisects both vertex angles.
Vertex Angles
Non-vertex Angles

25. References
E-Math 9 - Work Text in Mathematics (Rex Book Store)
Math Ideas and Life Applications 9 - Second Edition (Abiva)
Spiral Math 9 – (Trinitas Publishing Inc.)
Lesson 2