Download 7 Mastering the Standards Mastering the Standards

Hayes
®
Grade
AM109R
Mastering the Standards
GEOMETRY
By Murney R. Bell
7+
Mastering the Standards
Geometry
By Murney R. Bell
Illustrated by Reneé Yates
© Copyright 2008, Hayes School Publishing Co., Inc., Printed in USA
All rights reserved. The purchase of this book entitles the individual teacher to reproduce the activities in this book for use
with children. No parts of these publications may be stored in a retrieval system or transmitted in any form by any means,
electronic, mechanical, recorded, or otherwise, without prior written permission of Hayes School Publishing Co., Inc.
TABLE OF CONTENTS
Letter to Teachers and Parents...........................................................1
Lines and Angles
Teacher Overview...............................................................................2
Practice Assessment: Lines and Angles..............................................3
Points, Lines, and Planes....................................................................4
Intersections........................................................................................5
Measurement of Segments.................................................................6
Measurement of Angles......................................................................7
Bisectors of Segments..........................................................................8
Bisectors of Angles..............................................................................9
Angle Bisectors and Perpendicular Bisectors...................................10
Complementary and Supplementary Angles..................................11
Vertical Angles..................................................................................12
Equality and Congruence Properties................................................13
Relationships Between Lines............................................................14
Perpendicular Lines..........................................................................15
Parallel Lines....................................................................................16
Medians of a Triangle.......................................................................17
Transversals and Angles Formed.....................................................18
2-D Figures
Practice Assessment: 2-D Figures......................................................19
Polygons............................................................................................20
Classifying Polygons.........................................................................21
Angles in Polygons...........................................................................22
Properties of Parallelograms............................................................23
Area of Parallelograms and Rectangles...........................................24
Rectangles, Rhombuses, and Squares..............................................25
Trapezoids.........................................................................................26
Area of Triangles and Trapezoids.....................................................27
Parts of a Circle.................................................................................28
Arcs and Central Angles...................................................................29
Inscribed Angles................................................................................30
Circumference of Circles...................................................................31
Area of Circles...................................................................................32
Triangles
Practice Assessment: Triangles.........................................................33
Classifying Triangles.........................................................................34
Isosceles and Equilateral Triangles..................................................35
Triangle Inequalities.........................................................................36
Angle Measure of Triangles..............................................................37
Translations......................................................................................38
Pythagorean Theorem......................................................................39
Distance Formula.............................................................................40
Similar Triangles...............................................................................41
Similar Triangles and Proportions...................................................42
Sine and Cosine Ratios.....................................................................43
Tangent Ratios..................................................................................44
Solving Right Triangles.....................................................................45
Triangle Congruence........................................................................46
Triangle Congruence by SSS.............................................................47
Triangle Congruence by SAS............................................................48
Triangle Congruence by ASA...........................................................49
Using Congruent Triangles...............................................................50
Reflections and Symmetry................................................................51
Dilations............................................................................................52
3-D Figures
Practice Assessment: 3-D Figures......................................................53
Three-Dimensional Figures...............................................................54
Surface Area of Prisms and Cylinders..............................................55
Surface Area of Pyramids and Cones...............................................56
Volume of Prisms..............................................................................57
Volume of Cylinders.........................................................................58
Volume of Pyramids and Cones.......................................................59
Volume of Prisms, Cylinders, Pyramids, and Cones........................60
Surface Area and Volume of Spheres...............................................61
INTRODUCTION
This book contains standards-based problems similar to those
students will find on mastery tests in mathematics. The problems
are based on standards from the National Council of Teachers of
Mathematics and state standards from across the nation. Practice
pages include problems in Number and Operations, Algebra,
Geometry, Measurement, and Data Analysis and Probability. Each
section features a test for assessment and essential mathematical
vocabulary terms for success. Problem solving is embedded
throughout. One word problem on most pages requires a written
response on a separate piece of paper.
The activities may be used at any time of the year to assess
understanding, for additional practice, or for test preparation.
MASTERING THE STANDARDS: GEOMETRY 1
Name
Date
Practice Assessment: Lines and Angles
In the figure to the right, name four angles.
1.______
2.______
3.______
4.______
F
Using a protractor, measure the angles you
named in the above problems.
5.______
6.______
7.______
8.______
Give the complementary and supplementary angle to the angles measured.
9. ______ ______
12. ______ ______
10. ______ ______
13. ______ ______
11. ______ ______
Lines m and n are parallel and line l is a transversal. In this figure, name the following:
14.All pairs of corresponding angles_________
15.All pairs of alternate interior angles_ ______
16.All pairs of alternate exterior angles_______
l
In the figure to the right, give a reason
_why each statement is true.
17.∠UPO ≅ ∠WPV_______________________
18.∠WPU ≅ ∠WOS______________________
19.∠WPU ≅ ∠ROT_______________________
20.∠UPO ≅ ∠TOR_______________________
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Name
Date
Points, Lines, and Planes
Use the figure at the right. Name each of the following.
1.Four segments that intersect AB______________________
2.Three segments parallel to AB _ _____________________
3.Four segments skew to AB _ ________________________
4.Two planes with edge AB ___________________________
Use the figure at the right. Name each of the following.
5.All points________________________________________
6.Six line segments_ ________________________________
7.Four rays________________________________________
8.Two lines________________________________________
Write an equation that expresses each length. Then find the length of each line segment.
9.equation: ______
x = ______
AB ______ AC _____
10.equation: ______
n = ______
LM ______ MN ______
11.equation: ______
y = ______
RS______
ST______
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Name
Date
Intersections
point C on line AB
AB
point R at the start of ray RT
RT
points M and N at end of line segment MN
MN
C
R
T
M
N
Points are at intersections of lines, line segments,
and rays. With intersections, angles are formed.
Angles are named in several ways:
angle ABC (∠ABC)
angle CBA (∠CBA)
angle B (∠B)
angle 2 (∠2)
Name the figure and write the symbol for it.
1.
3.
____________________________
____________________________
2.
4.
____________________________
____________________________
Name each angle in four ways.
5.
7.
____________________________
6.
____________________________
8.
____________________________
___________________________
Give four examples of intersecting lines. (Example: The top edge of your math textbook and
the side edge.)
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