Geometry Grades 6–8

51 Pages·1995·0.539 MB·English

by  Janice Wendling

MP4056
Grades 6-8
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6.5cm
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Milliken Publishing Co. (cid:127) St. Louis, Missouri
Geometry
Grades 6–8
Pythagoras would be proud!
The theorems and principles of basic geometry
are clearly presented in this workbook, along
with examples and exercises for practice.
All concepts are explained in an easy–to–
Author
understand fashion to help students grasp
Janice Wendling
geometry and form a solid foundation for
Artist advanced learning in mathematics.
Elizabeth Adams
Each page introduces a new concept, along with
Editing and Page Design
a puzzle or riddle which reveals a fun fact.
Martha Kranes
Thought–provoking exercises encourage
Cover Design students to enjoy working the pages while
Gray Communications & gaining valuable practice in geometry.
Marketing
Project Director
Kathleen Hilmes
The purchase of this book entitles the individual purchaser
to reproduce copies by duplicating master or by any
Copyright © 1995 photocopy process for single classroom use.The
Milliken Publishing Company reproduction of any part of this book for commercial resale
11643 Lilburn Park Dr. or for use by an entire school or school system is strictly
St. Louis, MO 63146 prohibited. Storage of any part of this book in any type of
All rights reserved. electronic retrieval system is prohibited unless purchaser
www.millikenpub.com receives written authorization from the publisher.
Geometry Workbook
Table of Contents
Reading Mathematics . . . . . . . . . . . . . . . . . . .1 Trigonometric Ratios . . . . . . . . . . . . . . . . . . . . . .23
Undefined Terms and Basic Definitions . . . . .2 Perimeter . . . . . . . . . . . . . . . . . . . . . . . . . . .24
Types of Angles . . . . . . . . . . . . . . . . . . . . . . .3 Area of Rectangles and Triangles . . . . . . . . .25
Complementary and Supplementary Angles . . .4 Area of Trapezoids . . . . . . . . . . . . . . . . .26-27
Parallel, Perpendicular, and Skew Lines . . . .5 Area of Parallelograms . . . . . . . . . . . . . .28-29
Angles Formed by Parallel Lines . . . . . . . . . .6 Word Search . . . . . . . . . . . . . . . . . . . . . . . . .30
Angle Sum Theorem . . . . . . . . . . . . . . . . . . . .7 Circumference . . . . . . . . . . . . . . . . . . . . . . . .31
Exterior Angle Theorem . . . . . . . . . . . . . . . . .8 Area of a Circle . . . . . . . . . . . . . . . . . . . . . . .32
Classifying Triangles . . . . . . . . . . . . . . . . . . . .9 Area of Irregular Shapes . . . . . . . . . . . . . . . .33
The Pythagorean Theorem . . . . . . . . . . .10-11 Area of a Shaded Region . . . . . . . . . . . . . . .34
The Converse of the Pythagorean Theorem . . .12 Three–Dimensional Figures . . . . . . . . . . . . .35
Congruent Figures . . . . . . . . . . . . . . . . . . . .13 Surface Area of Right Prisms . . . . . . . . . . . .36
Congruent Triangles . . . . . . . . . . . . . . . . . . .14 Volume of Rectangular Prisms . . . . . . . . . . .37
Congruent Triangles . . . . . . . . . . . . . . . . . . .15 Volume of Right Prisms . . . . . . . . . . . . . . . .38
Angle and Triangle Word Search . . . . . . . . .16 Surface Area of Regular Pyramids . . . . . . . .39
Types of Quadrilaterals . . . . . . . . . . . . . . . . .17 Volume of Regular Pyramids . . . . . . . . . . . .40
Properties of Parallelograms . . . . . . . . . . . . .18 Surface Area of Cylinders . . . . . . . . . . . . . . .41
Properties of Rectangles, Rhombuses, Surface Area of Cones . . . . . . . . . . . . . . . . .42
and Squares . . . . . . . . . . . . . . . . . . . . . . . .19 Volume of Cylinders and Cones . . . . . . . . . .43
Trapezoids . . . . . . . . . . . . . . . . . . . . . . . . . .20 Crossword Puzzle . . . . . . . . . . . . . . . . . . . . .44
Ratio and Proportion . . . . . . . . . . . . . . . . . . .21 Answer Key . . . . . . . . . . . . . . . . . . . . . . .45-48
Similar Figures . . . . . . . . . . . . . . . . . . . . . . .22
© Milliken Publishing Company MP4056
Reading Mathematics
Remember:
Learning the correct meaning and use of mathematical symbols is necessary for reading
and understanding mathematics. In geometry, the order of the letters is important in some
cases, like when naming rays and angles.
Find the corresponding symbols and shade their areas to reveal a number that is neither prime
nor composite.
1. line AB 14. angle with vertex at C
2. segment AB 15. cosine of angle X
3. angle with vertex at B 16. is approximately equal to
4. triangle ABC 17. is similar to
5. cube root 18. greater than
6. arc AB 19. square root
7. ray AB 20. is congruent to
8. circle with center A 21. pi
9. tangent of angle X 22. is perpendicular to
10. not equal to 23. parallelogram ABCD
11. is parallel to 24. sine of angle X
12. right angle 25. less than
13. measure of angle A 26. ordered pair
© Milliken Publishing Company 1 MP4056
Undefined Terms and Basic Definitions
Geometry is based on the undefined terms point, line, and plane.
Points can be collinear (lie on the same line).
Points and lines can be coplanar (lie in the same plane).
A ray is part of a line with one endpoint.
An angle is formed by two rays that have the same endpoint.
Refer to the diagrams and determine whether the statement is true or false. If it is true, place its
corresponding letter in the puzzle to reveal the name of a famous mathematician and his
collection of books about geometry, number theory, and geometric algebra.
1. CK intersects RL at O. E 14. NJ and NH are opposite rays. E
2. M lies in plane X. A 15. ZL intersects RO at O. F
3. R, O, K, and A are coplanar. R 16. GF intersects JH at N. L
4. OR and OK are sides of ∠ROK. U 17. Plane E contains ∠JNF. I
5. A, O, and B are collinear. C 18. Plane D and Plane E intersect in GF. E
6. O, L, K, and M are coplanar. H 19. G, N, F, and P are coplanar. M
7. C, O, A, and B are coplanar. L 20. Q, H, N, and F are coplanar. E
8. Plane D contains P. P 21. N and P are in plane D. I
9. Plane X intersects AB at O. I 22. ∠GNH lies in plane D. N
10. A, B, and M are coplanar. D 23. G, N, and F are collinear. T
11. Plane X contains Z. S 24. Plane D contains PQ. B
12. J, N, F, and P are coplanar. A 25. NF and NG are opposite rays. S
13. ∠CBO lies in plane X. K
E

A
X
F
R K
D
O
Q
L J N H
C Z
G
M
B
P

© Milliken Publishing Company 2 MP4056
Types of Angles
An acute angle measures between 0° and 90°.
A right angle measures exactly 90°.
An obtuse angle measures between 90° and 180°.
A straight angle measures exactly 180°.
Refer to the diagram and classify each expression as acute, right, obtuse, or straight.
1. ∠CDL __________________________ 11. ∠EDA + ∠ADL _____________________
2. ∠EAD __________________________ 12. ∠ECD + ∠DCL _____________________
3. ∠DAB __________________________ 13. ∠ADE + ∠EDC _____________________
4. ∠CLD __________________________ 14. ∠UEC + ∠CEL _____________________
5. ∠ABI ___________________________ 15. ∠EDC + ∠CDL _____________________
6. ∠CLI ___________________________ 16. ∠ABD + ∠DBL _____________________
7. ∠UCL __________________________ 17. ∠CDE + ∠EDB _____________________
8. ∠ABL __________________________ 18. ∠EDA + ∠ADB _____________________
9. ∠ECL __________________________ 19. ∠EDA + ∠ADB + ∠EDC ______________
10. ∠AED __________________________ 20. ∠LDB + ∠BDA + ∠ADE ______________
E
A
B
I
D
U C L
© Milliken Publishing Company 3 MP4056
Complementary and Supplementary Angles
Remember:
alphabetic order numeric order
complementary 90°
ADD TO
supplementary 180°
Use a ruler to match each angle to its complement and its supplement. Each line you
draw will cross a letter. The letters without lines through them spell the answer.
Michael Jordan scored his career 20,000th point in Chicago.
In what cities did he score his 5,000th, 10,000th, and 15,000th points?
Complement Angle Supplement
47° A 52° 167°
L U
H C
C
63° 78° 137°
D G C
38° 13° 117°
L M
71° 43° K 102°
C A
12° H 27° 128°
D
E
L
83° 63° 161°
H
G D
77° G 7° 158°
I
C L
79° 19° 146°
N
T
56° 68° T 153°
P
L
27° 34° 103°
H
O
22° P 11° R O 112°
68° H 81° I 173°
C O
R
9° 77° T 169°
13° W I 22° A O 99°
____ ____ ____ ____ ____
____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____
© Milliken Publishing Company 4 MP4056
Parallel, Perpendicular, and Skew Lines
Parallel lines are coplanar lines that never intersect.
Skew lines are noncoplanar lines (neither parallel nor intersecting).
Perpendicular lines intersect to form right angles.
Planes can also be parallel, perpendicular, or intersecting.
Determine whether the following pairs of lines are parallel, perpendicular, skew, or
intersecting (not perpencicular). The figure is a cube—all faces are squares. Place the correct
corresponding letter in the blanks below to reveal the mathematician who developed hyperbolic
geometry. r r
a a
ul g ul
c n c g
parallel perpendiskew intersecti parallelperpendiskew ntersectin
i
1. AB and FG N P A D 10. HC and AB B F O M
2. AG and PQ E B J I 11. GD and AB I T A X
3. FE and FG Z K Q A 12. FG and GD L C F D
4. CD and HE O C V B 13. FE and BC H A E D
5. AG and HD L E M K 14. AB and AG R D L E
6. PQ and HD O Y A R 15. GB and DE N Q V P
7. AH and HC P I T W 16. EH and DH U W G S
8. HD and JK T U Y L 17. HC and BC K K I L
9. FG and BC H E O B 18. AG and JK D C Y H
A P B
X
____ ____ ____ ____ ____ ____ ____
1 2 3 4 5 6 7
F G
Q
H J C
____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____
8 9 10 11 12 13 14 15 16 17 18
Y
E K D
© Milliken Publishing Company 5 MP4056
Angles Formed by Parallel Lines
If two parallel lines are cut by a transversal, the resulting angles will either be
congruent or supplementary.
congruent angles supplementary angles
vertical angles adjacent angles
corresponding angles same–side interior angles
alternate interior angles same–side exterior angles
alternate exterior angles
Determine whether the angles listed are conguent, supplementary, or neither. If the
angles are congruent, write the corresponding letters in the top box below. If the angles
are supplements, write the corresponding letters in the lower box below.
1. ∠1 and ∠5 I 11. ∠4 and ∠7 F 21. ∠2 and ∠13
I
2. ∠1 and ∠6 G 12. ∠11 and ∠16 R 22. ∠4 and ∠8
W
3. ∠1 and ∠3 E 13. ∠5 and ∠6 C 23. ∠9 and ∠14 B
4. ∠5 and ∠10 O 14. ∠7 and ∠12 I 24. ∠1 and ∠13 T
5. ∠3 and ∠16 T 15. ∠10 and ∠14 N 25. ∠3 and ∠8 N
6. ∠7 and ∠11 S 16. ∠10 and ∠13 E 26. ∠3 and ∠15 O
7. ∠4 and ∠16 A 17. ∠1 and ∠14 D 27. ∠12 and ∠15 I
8. ∠6 and ∠9 T 18. ∠8 and ∠12 E 28. ∠5 and ∠9 N
9. ∠9 and ∠12 U 19. ∠2 and ∠5 L 29. ∠6 and ∠7 D
10. ∠6 and ∠10 A 20. ∠8 and ∠11 E 30. ∠4 and ∠15 Z
The creators of calculus were: l
k
(congruent)
__ __ __ __ __ __ __ __ __
1 2 3 4 m
__ __ __ __ __ __ __ 5 6 7 8
m || n
AND
(supplementary)
9 10 11 12 n
__ __ __ __ __ 13 14 15 16
__ __ __ __ __ __
© Milliken Publishing Company 6 MP4056
Angle Sum Theorem
The three angles of a triangle add to 180°.
Find the missing angle measure for each triangle. Use the decoder to read the message
below.
DECODER
1. 25°, 65°, _______ A = 90°
2. 42°, 120°, _______ C = 111°
3. 37°, 90°, _______ E = 135°
4. 23°, 46°, _______ F = 95°
5. 50°, 105°, _______ G = 24°
6. 136°, 20°, _______ H = 100°
7. 15°, 30°, _______ I = 53°
8. 30°, 45°, _______ L = 93°
9. 52°, 35°, _______ M = 86°
10. 67°, 13°, _______ N = 18°
11. 74°, 100°, _______ O = 6°
12. 9°, 110°, _______ P = 130°
13. 24°, 26°, _______ R = 25°
14. 10°, 84°, _______ S = 61°
15. 17°, 25°, _______ T = 105°
16. 40°, 45°, _______ U = 138°
17. 53°, 35°, _______ Y = 92°
____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____
8 10 7 1 4 15 8 7 1 2 6 9 7 12
____ ____ ____ ____ ____ ____ ____ ____
11 16 1 5 3 6 10 8
____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____
8 5 3 1 2 6 9 7 1 5 7
____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____
4 11 14 13 9 7 14 7 2 8 1 5 17
© Milliken Publishing Company 7 MP4056