Solutions Manual for Geometry: A High School Course By S. Lang and G
This book presents the worked-out solutions for all the exercises in the text by Lang and Murrow. It will be of use not only to mathematics teachers, but also to students using the text for self-study.
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Geometry: A High School Course by S. Lang and G. Murrow
Philip Carlson
Solutions Manual for
Geometry: A High School Course by S. Lang and G. Murrow With 100 Figures
Springer Science+Business Media, LLC
Philip Carlson General College University of Minnesota Minneapolis, MN 55455-0434 USA
Mathematics Subject Classification (1991): 02/04, 02/05 Library of Congress Cataloging-in-Publication Data Carlson, Philip. Solutions manual for geometry: a high school course by S. Lang and G. Murrow/Philip Carlson. p. cm. Includes bibliographical references. ISBN 978-0-387-94181-3 ISBN 978-1-4612-0861-7 (eBook) DOI 10.1007/978-1-4612-0861-7
1. Geometry, Plane-Problems, exercises, etc. 1994 QA459.C24 516.2-dc20
I. Title.
93-38093
Printed on acid-free paper. © 1994 Springer Science+Business Media N ew York Originally published by Springer-Verlag New York, Ine in 1994 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher Springer Seienee+Business Media, LLC , except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely byanyone.
Production managed by Francine McNeill; manufacturing supervised by Vincent Scelta. Camera-ready copy prepared by the author. 987654321 ISBN 978-0-387-94181-3
Contents
CHAPTER 1
Distance and Angles
1
CHAPTER 2
Coordinates CHAPTER 3
Area and the Pythagoras Theorem
21
27
CHAPTER 4
The Distance Formula
38
CHAPTER 5
Some Applications of Right Triangles
43
CHAPTER 6
Polygons ............. .....................................................
53
CHAPTER 7
Congruent Triangles
56
CHAPTER 8
Dilations and Similarities
64
CHAPTER 9
Volumes
..................................................................
80
CHAPTER 10
Vectors and Dot Products
85 v
vi
CONTENTS
CHAPTER 11
Transformations
98
CHAPTER 12
Isometrics
114
CHAPTER 1
Distance and Angles
§
1. Exercises
(Pages 5,6) l.
2.
a.
P-
-Q
h.
P",
Q
c.
P
Q
d.
P
»Q
a.
p h.
~,
The two rays, RpM and RPQ, form a whole line if M, P and Q are collinear and P lies between M and Q.
+ d(Q,M)
d(P,M)
3.
d(P,Q)
4.
AB is not parallel to PQ because LAB is not parallel to LPQ.
5.
Line segments connecting any three points in the plane do not necessarily form a triangle since the three points may be collinear.
=
1
2
GEOMETRY: SOLUTION MANUAL
6.
If line L were parallel to line U there would be 2 lines parallel to line U passing through the point P. This contradicts PAR 2. Therefore line L is not parallel to line U and must intersect it.
7.
B
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