Week 2 -Trapezoid and Kite.pptx

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