1. Section 6.6
Trapezoids and Kites

2. A trapezoid is a quadrilateral with exactly one pair of parallel sides
A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases. The nonparallel sides are called legs. The base angles are formed by the base and one of the legs. In trapezoid ABCD, ÐA and ÐB are one pair of base angles and ÐC and ÐD are the other pair. If the legs of a trapezoid are congruent, then it is an isosceles trapezoid.

3. Concept 1

4. Example 1: Each side of the basket shown is an isosceles trapezoid
Example 1: Each side of the basket shown is an isosceles trapezoid. If mJML = 130, KN = 6.7 feet, and LN = 3.6 feet,
a) find mMJK.
because….
mÐJML + mÐMJK = 180 because….
130 + mÐMJK = 180 because….
mÐMJK = ______ because….
JKLM is a trapezoid
Consec. Int. Angles Theorem
substitution
50°
Subtract 130 from each side

5. Example 1: Each side of the basket shown is an isosceles trapezoid
Example 1: Each side of the basket shown is an isosceles trapezoid. If mJML = 130, KN = 6.7 feet, and JL = 10.3 feet,
b) find MN.
because….
JL = KM because….
JL = KN + MN because….
10.3 = MN because….
JKLM is an isosceles trapezoid
Definition of congruent segments
Segment Addition
Substitution
3.6 = MN Subtract 6.7 from each side

6. Example 2: Quadrilateral ABCD has vertices A(5, 1),
B(–3, –1), C(–2, 3), and D(2, 4). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid.

7. Since the legs are not congruent, ABCD is not an isosceles trapezoid.

8. The midsegment of a trapezoid is the segment that connects the midpoints of the legs of the trapezoid.

9. Example 3: In the figure, MN is the midsegment of trapezoid FGJK
Example 3: In the figure, MN is the midsegment of trapezoid FGJK. What is the value of x?

10. A kite is a quadrilateral with exactly two pairs of consecutive congruent sides. Unlike a parallelogram, the opposite sides of a kite are not congruent or parallel.

11. Example 4:
a) If WXYZ is a kite, find mXYZ.
WXY  WZY because …
mWZY = ________
mW + mX + mY + mZ = _____ because …
a kite has one pair of  angles which
are between the two non-congruent sides.
121° substitution
360° polygon int.
angles sum
theorem
73° + 121° + mY + 121° = 360° Substitution
mY = 45° Simplify

12. Example 4:
b) If MNPQ is a kite, find NP.
(NR)2 + (MR)2 = (MN)2 because…Pythagorean Theorem
(6)2 + (8)2 = MN2 Substitution
= MN2 Simplify.
100 = MN2 Add.
10 = MN Take the square root of each side.
MN = NP Consecutive sides of a kite are congruent.
10 = NP Substitution

13. Example 4:
c) If BCDE is a kite, find mCDE.
C  E, and the sum of the interior angles of a kite is
360°, so to find the measure of D = 360 – 130 – 130 – 64.
mD = 36°