1. The document provides definitions and properties of kites and trapezoids, including that a kite has two pairs of congruent consecutive sides and a trapezoid has one pair of parallel sides. 2. Two examples show using properties of kites and trapezoids to solve problems, such as finding missing angle measures in a kite and finding side lengths in isosceles trapezoids. 3. The trapezoid midsegment theorem states that the midsegment of a trapezoid is half the sum of the legs, and this is used to find a missing side length in one example.

1. GT Geometry 2/12/14
Drill Put HW and pen on the corner of
your desk
Solve for x.
5 or –5
1. x2 + 38 = 3x2 – 12
43
2. 137 + x = 180
156
3.
4. Find FE.

2. Objectives
Use properties of kites to solve
problems.
Use properties of trapezoids to solve
problems.

3. Vocabulary
kite
trapezoid
base of a trapezoid
leg of a trapezoid
base angle of a trapezoid
isosceles trapezoid
midsegment of a trapezoid

4. A kite is a quadrilateral with exactly two pairs of
congruent consecutive sides.

5. A trapezoid is a quadrilateral with exactly one pair of
parallel sides. Each of the parallel sides is called a
base. The nonparallel sides are called legs. Base
angles of a trapezoid are two consecutive angles
whose common side is a base.

6. If the legs of a trapezoid are congruent, the trapezoid
is an isosceles trapezoid. The following theorems
state the properties of an isosceles trapezoid.

9. The midsegment of a trapezoid is the segment
whose endpoints are the midpoints of the legs. In
Lesson 5-1, you studied the Triangle Midsegment
Theorem. The Trapezoid Midsegment Theorem is
similar to it.

11. Example 1: Problem-Solving Application
Lucy is framing a kite with
wooden dowels. She uses two
dowels that measure 18 cm,
one dowel that measures 30
cm, and two dowels that
measure 27 cm. To complete
the kite, she needs a dowel to
place along . She has a dowel
that is 36 cm long. About how
much wood will she have left
after cutting the last dowel?

12. Example 1 Continued
3
Solve
N bisects JM.
Pythagorean Thm.
Pythagorean Thm.

13. Example 1 Continued
Lucy needs to cut the dowel to be 32.4 cm long.
The amount of wood that will remain after the
cut is,
36 – 32.4
3.6 cm
Lucy will have 3.6 cm of wood left over after the
cut.

14. Example 2A: Using Properties of Kites
In kite ABCD, m DAB = 54°, and
m CDF = 52°. Find m BCD.
Kite  cons. sides
∆BCD is isos.
CBF
CDF
m CBF = m CDF
2
sides isos. ∆
isos. ∆ base
Def. of
s
s
m BCD + m CBF + m CDF = 180° Polygon
Sum Thm.

15. Example 2A Continued
m BCD + m CBF + m CDF = 180°
Substitute m CDF
m BCD + m CDF + m CDF = 180°
for m CBF.
m BCD + 52° + 52° = 180°
m BCD = 76°
Substitute 52 for
m CDF.
Subtract 104
from both sides.

16. Example 3A: Using Properties of Isosceles
Trapezoids
Find m A.
m C + m B = 180°
100 + m B = 180
Same-Side Int.
s Thm.
Substitute 100 for m C.
m B = 80°
A
B
Subtract 100 from both sides.
Isos. trap. s base
m A=m B
Def. of
m A = 80°
Substitute 80 for m B
s

17. Example 3B: Using Properties of Isosceles
Trapezoids
KB = 21.9 and MF = 32.7.
Find FB.
Isos.  trap.
KJ = FM
Def. of
s base
segs.
KJ = 32.7 Substitute 32.7 for FM.
KB + BJ = KJ
Seg. Add. Post.
21.9 + BJ = 32.7 Substitute 21.9 for KB and 32.7 for KJ.
BJ = 10.8 Subtract 21.9 from both sides.

18. Example 5: Finding Lengths Using Midsegments
Find EF.
Trap. Midsegment Thm.
Substitute the given values.
EF = 10.75
Solve.