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

2. TRAPEZOID
Definition: 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 are two consecutive angles on a common 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.

3. PROPERTIES “OF”

4. Using Properties of Isosceles Trapezoids
Reflexive
Isos. trap. 
base s 
KFJ  MJF
Isos. trap. 
legs 
∆FKJ  ∆JMF
SAS
In an isosceles trapezoid corresponding parts of the congruent diagonals are congruent.
BKF  BMJ
CPCTC
FBK  JBM
Vert. s 
∆FBK  ∆JBM
AAS
CPCTC

5. Check It Out! Example 3a
Find mF.
mF + mE = 180°
Same-Side Int. s Thm.
E  H
Isos. trap. s base 
mE = mH
Def. of  s
mF + 49° = 180°
Substitute 49 for mE.
mF = 131°
Simplify.
In an isosceles trapezoid opposite base angles
are supplementary

6. Example 4A: Applying Conditions for Isosceles Trapezoids
Find the value of a so that PQRS is isosceles.

7. 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.
ll to the bases
Average of the bases

8. Example 5: Finding Lengths Using Midsegments
Find EF.
Find EH.

9. Definition:
A kite is a quadrilateral with exactly two pairs of congruent consecutive sides (opposite sides not ).

10. PROPERTIES “OF”
One diagonal perpendicularly bisects the other

11. Example 2A: Using Properties of Kites
In kite ABCD, mDAB = 54°, and mCDF = 52°.
Find mBCD and mABC.

12. Check It Out! Example 2a
In kite PQRS, mPQR = 78°, and mTRS = 59°.
Find mQRT and mQPS.

13. Lesson Quiz: Part I
1. Erin is making a kite based on the pattern below. About how much binding does Erin need to cover the edges of the kite?
In kite HJKL, mKLP = 72°,
and mHJP = 49.5°. Find each
measure.
2. mLHJ 3. mPKL

14. Lesson Quiz: Part II
Use the diagram for Items 4 and 5.
4. mWZY = 61°. Find mWXY.
5. XV = 4.6, and WY = Find VZ.
6. Find LP.