Name ___________________________________________ Date _____________________ Class ____________________
6.6 Properties of Trapezoids and Kites
Unit 6: Polygons & Quadrilaterals
A kite is a quadrilateral with exactly two pairs of congruent
consecutive sides. If a quadrilateral is a kite, such as FGHJ,
then it has the following properties.
Properties of Kites
FH
GJ
m G=m J
Exactly one pair of opposite angles is
congruent.
The diagonals are perpendicular.
Mark the symbols on each figure to match the given definition.
1. Kites are quadrilaterals
with perpendicular
diagonals.
2. Kites are quadrilaterals with
exactly one pair of congruent
opposite angles.
3. Kites are quadrilaterals
with exactly two pairs of
congruent consecutive sides.
ABCD is a kite. Use the figure to find each measure.
4. m D
5. AB
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In kite ABCD, m BCD
6. CD
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98 , and m ADE
47 . Find each measure.
7. m DAE
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8. m BCE
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9. m ABC
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Name ___________________________________________ Date _____________________ Class ____________________
A trapezoid is a quadrilateral with exactly one pair of parallel sides. If the legs of
a trapezoid are congruent, the trapezoid is an isosceles trapezoid.
Each nonparallel side
is called a leg.
Each || side is
called a base.
Base angles are two same
side angles on either side
of a base.
Isosceles Trapezoid Properties
• Each pair of base angles is congruent.
• Its diagonals are congruent.
Mark the symbols on each figure to match the given definition.
10. Trapezoids are quadrilaterals with exactly
one pair of parallel sides.
11. Isosceles trapezoids are trapezoids
with congruent diagonals.
12. Isosceles trapezoids are trapezoids
with congruent legs.
13. Isosceles trapezoids are trapezoids with
two pairs of congruent base angles.
Find each value.
14. Find m J in trapezoid JKLM.
15. In trapezoid EFGH, FH
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9. Find AG.
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Find each value so that the trapezoid is isosceles.
16. Find the value of x.
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17. AC 2z + 9, BD
value of z.
4z
3. Find the
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Name ___________________________________________ Date _____________________ Class ____________________
Trapezoid Midsegment Properties
The midsegment of a trapezoid is the segment
whose endpoints are the midpoints of the legs.
• It is parallel to each base.
• The length of the midsegment is one-half
the sum of the length of the bases.
1
AB
(MN + LP)
2
AB is the
midsegment
of LMNP.
Find each length.
18. KL
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20. EF
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19. PQ
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21. WX
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The figure at right shows a ziggurat. A ziggurat is a stepped,
flat-topped pyramid that was used as a temple by ancient
peoples of Mesopotamia. The dashed lines show that a ziggurat
has sides roughly in the shape of a trapezoid.
22. Each “step” in the ziggurat has equal height. Give the vocabulary term for MN.
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23. The bottom of the ziggurat is 27.3 meters long, and the top of the ziggurat
is 11.6 meters long. Find MN.
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