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Name _______________________________________ Date ___________________ Class __________________
LESSON
6-6
Reteach
Properties of Kites and Trapezoids
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
G  J

Exactly one pair of opposite angles is
congruent.
The diagonals are perpendicular.
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
consecutive angles whose
common side is a base.
Isosceles Trapezoid Theorems
• In an isosceles trapezoid, each pair of base angles is congruent.
• If a trapezoid has one pair of congruent base angles, then it is isosceles.
• A trapezoid is isosceles if and only if its diagonals are congruent.
In kite ABCD, mBCD  98, and mADE  47. Find each measure.
1. mDAE
________________________________________
2. mBCE
________________________________________
3. mABC
________________________________________
5. In trapezoid EFGH, FH  9. Find AG.
4. Find mJ in trapezoid JKLM.
________________________________________
________________________________________
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6-46
Holt Geometry
Name _______________________________________ Date ___________________ Class __________________
LESSON
6-6
Reteach
Properties of Kites and Trapezoids continued
Trapezoid Midsegment Theorem
The midsegment of a trapezoid is the segment
whose endpoints are the midpoints of the legs.
• The midsegment of a trapezoid is parallel to
each base. AB MN and AB LP
• 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 value so that the trapezoid is isosceles.
7. AC  2z  9, BD  4z  3. Find the
value of z.
6. Find the value of x.
________________________________________
________________________________________
Find each length.
8. KL
9. PQ
________________________________________
10. EF
________________________________________
11. WX
________________________________________
________________________________________
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6-47
Holt Geometry
Name _______________________________________ Date ___________________ Class __________________
LESSON
6-6
Practice A
Properties of Kites and Trapezoids
Fill in the blanks to complete each theorem or definition.
1. If a quadrilateral is a kite, then its ________________________ are perpendicular.
2. If a quadrilateral is a kite, then exactly one pair of opposite ________________________
are congruent.
3. A kite is a quadrilateral with exactly two pairs of congruent
consecutive ________________________.
ABCD is a kite. Use the figure to find each measure
in Exercises 4–6.
4. mD
5. AB
________________________
6. CD
________________________
________________________
A trapezoid is a quadrilateral with exactly one pair of
parallel sides. Name the parts of trapezoid PQRS
asked for in Exercises 7–9.
7. both bases
____________________
8. both legs
____________________
9. one pair of base angles
____________________
Fill in the blanks to complete each theorem or definition.
10. A trapezoid is isosceles if and only if its ____________________ are congruent.
11. If a trapezoid has one pair of congruent base angles, then the trapezoid
is ____________________.
12. If the legs of a trapezoid are ____________________, then the trapezoid is
an isosceles trapezoid.
13. If a quadrilateral is an isosceles trapezoid, then each pair of
____________________ is congruent.
In an art museum, a statue sits on a pedestal with sides that are
isosceles trapezoids. Name the parts of isosceles trapezoid EFGH
asked for in Exercises 14 and 15.
14. both pairs of congruent angles
_____________________________________
15. both pairs of congruent segments
_____________________________________
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6-44
Holt Geometry
Name _______________________________________ Date ___________________ Class __________________
LESSON
6-6
Practice B
Properties of Kites and Trapezoids
In kite ABCD, mBAC  35 and mBCD  44.
For Exercises 1–3, find each measure.
1. mABD
________________________
2. mDCA
3. mABC
________________________
________________________
4. Find the area of EFG. _____________________
6. KM  7.5, and NM  2.6. Find LN.
5. Find mZ.
________________________________________
________________________________________
7. Find the value of n so that PQRS is isosceles.
________________________________________
8. Find the value of x so that EFGH is isosceles.
________________________________________
9. BD  7a  0.5, and AC  5a  2.3. Find the
value of a so that ABCD is isosceles.
________________________________________
10. QS  8z2, and RT  6z2  38. Find the
value of z so that QRST is isosceles.
________________________________________
Use the figure for Exercises 11 and 12. The figure 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.
11. Each “step” in the ziggurat has equal height. Give the vocabulary term for MN.
________________________________________
12. 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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6-45
Holt Geometry
LESSON
6-6
Challenge
Investigating Darts
A dart is another type of geometric figure. Examples of darts are shown in the table.
Darts
Not Darts
1. Based on your observations of the figures in the table, write a definition of the
term dart.
________________________________________________________________________________________
________________________________________________________________________________________
2. Describe the similarities and differences between the properties of darts and kites.
________________________________________________________________________________________
________________________________________________________________________________________
3. Find the values of x and y so that GHJK is a dart.
________________________________________
4. Make a conjecture about the line that contains the
diagonal from the tip to the vertex of the tail of a dart
and the diagonal that joins the fin angles.
________________________________________
________________________________________
________________________________________
5. Make a conjecture about the two triangles formed by the tip-to-tail diagonal.
________________________________________________________________________________________
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Holt Geometry