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.
Definition: 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. PROPERTY “OF”
FOR
OF & FOR

4. OF PROPERTIES:
Trapezoid  Quad with EXACTLY 1 pair of opposite sides ║
Isosceles Trapezoid  legs 
Isosceles Trapezoid  base  pairs 
Isosceles Trapezoid  diags 
FOR PROPERTIES:
Quad with EXACTLY 1 pair of opposite sides ║  Trap
Trap AND Legs  → Isos Trap
Trap AND Diagonals  → Isos Trap
Trap AND 1 base  pairs  → Isos Trap

5. 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

6. 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

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

8. 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

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

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

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

12. Kite  Quad with exactly 2 pair ≅ consecutive sides
Kite → diagonals ⊥
Kite → Exactly 1 pair opposite angles ≅

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

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

15. 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

16. 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.