Transcript Slide 1

A kite is a quadrilateral with exactly
two pairs of congruent consecutive
sides.
Example 1:
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?
36 – 32.4  3.6 cm left
N
Example 2A: In kite ABCD, mDAB = 54°,
and mCDF = 52°. Find
mBCD.
Kite  cons. sides 
∆BCD is isos.
2  sides isos. ∆
CBF  CDF
isos. ∆ base s 
mCBF = mCDF
Def. of   s
mBCD + mCBF + mCDF = 180° Polygon  Sum Thm.
mBCD + mCBF + mCDF = 180°
mBCD + 52° + 52° = 180°
mBCD = 76°
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.
If the legs of a trapezoid are congruent, the trapezoid is an isosceles
trapezoid. The following theorems state the properties of an
isosceles trapezoid.
Example 3a Find mF.
mF + mE = 180°
E  H
mE = mH
mF + 49° = 180°
mF = 131°
Same-Side Int. s Thm.
Isos. trap. s base 
Def. of  s
Substitute 49 for mE.
Simplify.
Example 3b
JN = 10.6, and NL = 14.8.
Find KM.
Isos. trap. s base 
KM = JL
JL = JN + NL
Def. of  segs.
KM = JN + NL
Substitute.
Segment Add Postulate
KM = 10.6 + 14.8 = 25.4 Substitute and simplify.
Example 4
Find the value of x so that
PQST is isosceles.
Q  S
mQ = mS
Trap. with pair base
s   isosc. trap.
Def. of  s
2 + 19 for mQ
Substitute
2x
2x2 + 19 = 4x2 – 13 and 4x2 – 13 for mS.
32 = 2x2
x = 4 or x = –4
Subtract 2x2 and add
13 to both sides.
Divide by 2 and simplify.
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.
Example 5A
Find EF.
Trap. Midsegment Thm.
Substitute the given values.
EF = 10.75
Solve.
Example 5B
Find EH.
Trap. Midsegment Thm.
1
16.5 = 2 (25 + EH) Substitute the given values.
Simplify.
33 = 25 + EH
Multiply both sides by 2.
13 = EH
Subtract 25 from both sides.