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NOTES FOR LESSON 6-6: TRAPEZOIDS
A trapezoid is a quadrilateral with exactly one pair of parallel
sides. The two parallel sides are called bases. The two
nonparallel sides are called legs.
A pair of base angles share a common base.

1 and  2 are one pair of base angles.

 3 and  4 are a second pair of base angles.
The midsegment of a trapezoid is a segment connecting the
midpoints of the legs. (Theorem 6-21) The midsegment is:
1) parallel to the bases and
2) its length is half the sum of the lengths of the bases. (average of the base lengths)
MN =
1
(QR + ZX )
2
An isosceles trapezoid is a trapezoid in which the legs are congruent.
An isosceles trapezoid has some special properties:
1) Each pair of base angles is
congruent. (Theorem 6-19)
2) The diagonals are
congruent. (Theorem 6-20)
Exercises
1. In trapezoid LMNO, what is the measure of
OLM? What is the measure of LMN?
2. WXYZ is an isosceles trapezoid and WY = 12.
What is XZ?
3. XZ is the midsegment of trapezoid EFGH. If FG = 8 and
EH = 12, what is XZ?
4-5: Find the value of x and the length of each unknown leg and/or midsegment.
4. QR is the midsegment of trapezoid LMNP
L
4x -10
10
5. Q
M
2x + 11
M
Q
R
x+2
N
R
8x - 12
P
P
8
S
N
NOTES FOR LESSON 6-6: KITES
A kite is a quadrilateral in which two pairs of consecutive sides
are congruent and no opposite sides are congruent.
In a kite, the diagonals are perpendicular. (Theorem 6-22)
The diagonals look like the crossbars in the frame of a typical
kite that you fly.
Notice that the sides of a kite are the hypotenuses of four right
triangles whose legs are formed by the diagonals.
Exercises
In kite FGHJ in the problem, mJFK = 38 and mKGH = 63. Find the following angle
and side measures.
1. mFKJ
2. mFJK
3. mFKG
4. mKFG
5. mFGK
6. mGKH
7. mKHG
8. mKJH
9. mJHK
10. If FG = 4.25, what is JF?
11. If HG = 5, what is JH?
12. If JK = 8.5, what is GJ?
13. How many pairs of congruent triangles are there in kite FGHJ? Name the pairs of
triangles and state the "shortcut" (theorem/postulate) that can be used to prove each pair
congruent.