Download Answers for the lesson “Classify Polygons”

LESSON
1.6
Answers for the lesson “Classify Polygons”
Skill Practice
14. Student A: the hexagon is
concave, Student B: the hexagon
does not have congruent sides.
1. An n-gon is a polygon with
n sides.
2. Yes, the string will match the
sides of a convex polygon, so it
will be the perimeter of the
polygon; no, the length of the
string will be less than the
perimeter of the polygon.
3. polygon; concave
4. Not a polygon; part of the figure
is not a segment.
15. 8 in.
16. 1408
17. 3 ft
18. always
19. sometimes
20. always
21. never
22. always
23. never
24–27. Sample answer are given.
24.
5. polygon; convex
6. Not a polygon; some segments
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intersect more than two segments.
25.
7. C
8. Octagon; regular; it has 8
congruent sides and angles.
9. Pentagon; regular; it has 5
26.
congruent sides and angles.
10. Triangle; regular; it has 3
congruent sides and angles.
11. Triangle; none of these; the sides
27.
and/or the angles are not all
congruent.
12. Quadrilateral; equilateral; it has 4
congruent sides.
13. Quadrilateral; equiangular; it has
28. 4
29. 1
30. 50
4 congruent angles.
Geometry
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20
31. 728, 728, 368. Sample answer: To
find the measure of the angles of
the pentagon, solve 20x 1 48 5
33x 1 9. Since x 5 3, the measure
of an angle of the pentagon is 1088.
ŽABC and ŽACB form a
linear pair with an angle of a
pentagon so they are both equal to
1808 2 1088 5 728. ŽBAC,
ŽCAD, and ŽDAE must have a
sum of 1808. Since ŽCAB >
ŽDAE, 2y 1 108 5 180, y 5 36,
so mŽCAB 5 368.
Problem Solving
39. 105 mm; each side of the button
is 15 millimeters long, so the
perimeter of the button is
15(7) 5 105 millimeters.
40. a. Pentagon
5, 5
Hexagon
6, 9
Heptagon
7, 14
32. a. convex
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b. Octagon, it appears to
be regular.
The difference between the
successive number of
diagonals is increasing by one.
33. triangle; regular
34. quadrilateral; equiangular
35. octagon: regular
b. 20 diagonals; 27 diagonals.
Sample answer: The pattern
described continues.
36. dodecagon; none of these
37. C
c. 1710 diagonals
38. a– b. Sample:
triangle
convex
none
quadrilateral
convex
regular
pentagon
convex
none
heptagon
concave
none
octagon
concave
equiangular
Geometry
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21
41. a. 3
b. 5
c. 6
d. 8
42.
c. 558, ŽHGC > ŽHBG; 1258,
ŽDBG is supplementary to
ŽHBG; 1258, ŽFCG is
supplementary to ŽHCG.
4. 148;
1
4
Mixed Review of
Problem Solving
1. a. 108 ft2
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b. $81, $124.20
c. $43.20
2. Sample answer: GBC,
GBCDEFA; triangle, heptagon
3. a. Sample answer: ŽDGB and
ŽBGH, ŽHGC and ŽCGF,
ŽDBG and ŽHBG, ŽHCG
and ŽFCG, ŽDBG and
ŽHCG, ŽHBG and ŽFCG,
ŽHDG and ŽHGF
5. a. 108 bricks, about 98 bricks;
convert total perimeter to
inches and then divide by 10.
b. 3 bundles; 206 bricks are
needed, thus 3 bundles.
6. 7.5 ft of bamboo
b. 218, ŽFGC > ŽDGB; 698,
ŽBGH is complementary to
ŽDGB; 698, ŽHGC is
complementary to ŽFGC.
Geometry
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22
7. 378;
3
7
}
8. a. 8Ï 5 units
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b. 8 square units, 8 square units;
16 square units; The area of
the quadrilateral is the sum of
the areas of the two triangles.
Geometry
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