GEOMETRY By Murney R. Bell

Transcription

1 Hayes AM109R Mastering the Standards GEOMETRY By Murney R. Bell Grade 7 +

2 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 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 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

3 Practice Assessment: Lines and Angles In the figure to the right, name four angles F Using a protractor, measure the angles you named in the above problems Give the complementary and supplementary angle to the angles measured 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 3

4 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 4

5 point C on line AB point R at the start of ray RT points M and N at end of line segment MN Intersections AB RT MN 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) R M C T N Name the figure and write the symbol for it Name each angle in four ways Give four examples of intersecting lines. (Example: The top edge of your math textbook and the side edge.) 5