Lesson 1.4 • Polygons

Lesson 1.4 ? Polygons

Name

Period

Date

For Exercises 1?8, complete the table.

Polygon name Number of sides Number of diagonals

1. Triangle

2.

2

3.

5

4. Hexagon

5. Heptagon

6.

8

7.

35

8.

12

For Exercises 9?11, sketch and label each figure. Mark the congruences. 9. Concave pentagon PENTA, with external diagonal ET, and TA PE.

10. Equilateral quadrilateral QUAD, with Q U. 11. Regular octagon ABCDEFGH. For Exercises 12?15, sketch and use hexagon ABCDEF. 12. Name the diagonals from A. 13. Name a pair of consecutive sides. 14. Name a pair of consecutive angles. 15. Name a pair of non-intersecting diagonals. For Exercises 16?19, use these figures at right.

MNOPQ RSTUV

16. mN _____ 17. VR _____ 18. mP _____ 19. ON _____

O

Q P 8.4

7.2 M

T

61? U

16.1 V

N

82? 58?

S

R

20. How many different (noncongruent) convex quadrilaterals can you make on a 3-by-3 dot grid, using the dots as vertices?

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CHAPTER 1

Discovering Geometry Practice Your Skills ?2003 Key Curriculum Press

ANSWERS

LESSON 1.1 ? Building Blocks of Geometry

1. S

2. 9 cm

3. SN

5. NS

6. PQ

7. SP

8. KN KL, NM LM, NO LO

4. endpoint

9.

C

A 3.2 cm M

B

2.0 cm D

10.

B

2.5 cm

C 2.5 cm

A

5 cm

D

11. E(14, 15)

12. AB, AC, AD, AE, AF, BC, BD, BE, BF, CD, CE, CF, DE, DF, EF (15 lines)

5 cm

E

B

C

A

D

13. 2 lines

Z

X

Y

W

U

V

F

E

14. Possible coplanar set: {C, D, H, G}; 12 different sets

LESSON 1.2 ? Poolroom Math

1. the vertex 4. 126? 7. 47? 10. 110?

12. R

90? I

14. 90?

2. the bisector 3. a side

5. DAE

6. 133?

8. 63?

9. 70?

11. N

M

15?

O

13.

160?

z

G

15. 120?

16. 75?

17. mAPB would have to be 214?, which is larger than an angle measure can be.

18. First it increases, then it is undefined, then decreases, then undefined, then increases.

LESSON 1.3 ? What's a Widget?

1. e

2. d

3. f

4. c

5. g

6. k

7. b

8. i

9. j

10. l

11. h

12. a

13. Sample answers: sides of a road, columns, telephone poles

14. They have the same measure, 13?. Because mQ 77?, its complement has measure 13?. So, mR 13?, which is the same as mP.

15.

1

16. P

R

2

Q

3

17.

B

C

A

X

Y

LESSON 1.4 ? Polygons

Polygon name 1. Triangle 2. Quadrilateral 3. Pentagon 4. Hexagon 5. Heptagon 6. Octagon 7. Decagon 8. Dodecagon

Number of sides 3 4 5 6 7 8 10 12

Number of diagonals

0 2 5 9 14 20 35 54

9.

P

A

E N

T

10.

Q

D

U

A

Discovering Geometry Practice Your Skills ?2003 Key Curriculum Press

ANSWERS

87

11.

H

G

A B

F

C

E

D

12. AC, AD, AE

13. Possible answer: AB and BC

14. Possible answer: A and B 15. Possible answer: AC and FD

16. 82?

17. 7.2

18. 61?

20. 12

19. 16.1

LESSON 1.6 ? Circles 1.

O

B

A

D C

2. 48?

3. 132?

4. 228? 5. 312?

6. 30?

7. 105?

8. 6712?

9. The chord goes through the center, P. (It is

the diameter.)

P

10.

11.

LESSON 1.5 ? Triangles and Special Quadrilaterals

For Exercises 1?7, answers will vary. Possible answers are shown.

1. AB GH

2. EF BI

3. CG FH

4. EFH and IFH

5. DEG and GEF

6. DEG and GEF

7. ADC and EDG

8.

T

I

R

9.

R

M

H

O

10. C

L S

M A

N

11. T

P

R

E

A

12.

E

T

K

I

For Exercises 13?25, answers may vary. Possible answers are shown. 13. ACFD 14. ACIG 15. EFHG 16. EFIG 17. BFJD 18. BFHD 19. DHFJ 20. DFJ 21. ABD 22. ABD 23. D(0, 3) 24. E(0, 5) 25. F(8, 2) 26. G(16, 3)

12. (8, 2); (3, 7); (3, 3) 13.

180?

50? 290?

14. Kite

P

15.

B Q

A

88

ANSWERS

Discovering Geometry Practice Your Skills ?2003 Key Curriculum Press

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