Download Exercises 6-6 - Spokane Public Schools

6-6
6-6 Exercises
Exercises
KEYWORD: MG7 6-6
KEYWORD: MG7 Parent
GUIDED PRACTICE
Assignment Guide
−−
−−
RS and−−
PV;
bases:−−
legs: PR and VS;
−−
midsegment: QT
Assign Guided Practice exercises
as necessary.
If you finished Examples 1–2
Basic 13–16, 24, 25, 28, 29,
31
Average 13–16, 24, 25, 28, 29,
31, 37, 38
Advanced 13–16, 24, 25, 28, 29,
31, 37–39
SEE EXAMPLE
1
p. 428
If you finished Examples 1–5
Basic 13–34, 40–42, 45,
47–49, 52–56
Average 13–23, 24–32 even,
33–36, 38–42 even,
43–45, 47–49, 52–56
Advanced 13–23, 28–32 even,
33, 35–42, 44–56
Vocabulary Apply the vocabulary from this lesson to answer each question.
1. In trapezoid PRSV, name the bases,
the legs, and the midsegment.
,
-
+
/
2. Both a parallelogram and a kite have
two pairs of congruent sides. How are
the congruent sides of a kite different from
the congruent sides of a parallelogram?
*
6
3. Crafts The edges of the kite-shaped glass in
the sun catcher are sealed with lead strips.
JH, KH, and LH are 2.75 inches, and MH is
5.5 inches. How much lead is needed to
seal the edges of the sun catcher? If the
craftsperson has two 3-foot lengths of lead,
how many sun catchers can be sealed?
about 20.1 in.; 3 sun catchers
SEE EXAMPLE
2
p. 429
Homework Quick Check
In kite WXYZ, m∠WXY = 104°,
and m∠VYZ = 49°.
Find each measure.
8
9
4. m∠VZY 41°
Quickly check key concepts.
Exercises: 13, 14, 18, 20, 22,
28, 32
6
5. m∠VXW 63°
6. m∠XWZ 54°
SEE EXAMPLE
3
p. 430
Answers
2. Possible answer: In a , 2 pairs
of opp. sides are . In a kite,
exactly 2 distinct pairs of cons.
sides are .
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7
8. RW = 17.7, and SV = 23.3.
Find TW.
7. Find m∠A. 106°
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5.6
/
7
SEE EXAMPLE 4
p. 430
,
9. Find the value of z so
that EFGH is isosceles. 2 or -2
6
10. MQ = 7y - 6, and LP = 4y + 11.
Find the value of y so that
17 = 5 2
LMPQ is isosceles.
_
_
3
3
*
SEE EXAMPLE
5
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11. Find QR. 14
p. 431
+
12. Find AZ. 9.5
+
8
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9
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Ç°£
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432
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Chapter 6 Polygons and Quadrilaterals
LESSON
6-6
Practice A
6-6 PRACTICE A
Properties of Kites and Trapezoids
Fill in the blanks to complete each theorem or definition.
diagonals
1. If a quadrilateral is a kite, then its
are perpendicular.
angles
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
ge07se_c06_0427_0435.indd 432
consecutive
sides
.
9/12/05 11:45:42 AM
$
3.25
ABCD is a kite. Use the figure to find each measure
in Exercises 4–6.
!
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118°
6
"
4. mD
5. AB
6. CD
118
3.25
6
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A trapezoid is a quadrilateral with exactly one pair of
parallel sides. Name the parts of trapezoid PQRS
asked for in Exercises 7–9.
1
3
2
_ _
PQ
SR
_ ;_
PS ; QR
S and R or
P and Q
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
diagonals or legs or
base s
are congruent.
11. If a trapezoid has one pair of congruent base angles, then the trapezoid
is
isosceles
.
12. If the legs of a trapezoid are
an isosceles trapezoid.
congruent
, then the trapezoid is
13. If a quadrilateral is an isosceles trapezoid, then each pair of
KEYWORD: MG7 Resources
432
Chapter 6
base angles
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.
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14. both pairs of congruent angles
HEF GFE; EHG FGH
15. both pairs of congruent segments
EH FG ; EG FH
_
_ _
_
PRACTICE AND PROBLEM SOLVING
13
14–16
17–18
19–20
21–22
1
2
3
4
5
""
Çʈ˜°
13. Design Each square section in the iron railing
contains four small kites. The figure shows
the dimensions of one kite. What length of
iron is needed to outline one small kite?
How much iron is needed to outline one
complete section, including the square?
Independent Practice
For
See
Exercises Example
Çʈ˜°
Çʈ˜°
In Exercises 27−32, students may
not be sure how to begin solving the
problem. Point out that they must
first determine if the figure is a kite,
a trapezoid, or an isosceles trapezoid. Then suggest that they redraw
each figure, marking known properties for that type of quadrilateral.
£Çʈ˜°
about 56.6 in.; about 418.3 in.
In kite ABCD, m∠DAX = 32°, and m∠XDC = 64°.
Find each measure.
Extra Practice
14. m∠XDA 58°
Skills Practice p. S15
15. m∠ABC 122°
Ê,,",
,/
16. m∠BCD 52°
8
Application Practice p. S33
18. SZ = 62.6, and KZ = 34. Find RJ. 96.6
17. Find m∠Q. 62°
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19. Algebra Find the value of a so that XYZW is isosceles.
Give your answer as a simplified radical. ±4 √
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9
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20. Algebra GJ = 4x - 1, and FH = 9x - 15. Find the value
of x so that FGHJ is isosceles. 2.8
21. Find PQ.
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22. Find KR.
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6
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ÎÓ°x
Tell whether each statement is sometimes, always, or never true.
23. The opposite angles of a trapezoid are supplementary. S
24. The opposite angles of a kite are supplementary. S
25. A pair of consecutive angles in a kite are supplementary. N
26. Estimation Hal is building a trapezoid-shaped
frame for a flower bed. The lumber costs $1.29
6 ft
per foot. Based on Hal’s sketch, estimate the cost
of the lumber. (Hint: Find the angle measures
60°
in the triangle formed by the dashed line.)
6 ft
20 ft
Possible answer: about $60
Find the measure of each numbered angle.
28. m∠1 = 116°;
m∠2 = 46°
27.
29. m∠1 = 51°;
m∠2 = 16°
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30.
30. m∠1 = 112°;
m∠2 = 40°
28.
£
m∠1 = 82°;
™n m∠2 = 128°
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m∠1 = 120°
m∠1 = 117°
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Lesson 6-6
433