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NAME DATE PERIOD,1 Reading to Learn Mathematics,Vocabulary Builder. This is an alphabetical list of the key vocabulary terms you will learn in Chapter 1. Vocabulary Builder, As you study the chapter complete each term s definition or description. Remember to add the page number where you found the term Add these pages to. your Geometry Study Notebook to review vocabulary at the end of the chapter. Vocabulary Term Definition Description Example,acute angle. adjacent angles,uh JAY suhnt,angle bisector,koh LIN ee uhr. complementary angles,kuhn GROO uhnt,koh PLAY nuhr,line segment.
linear pair,continued on the next page,Glencoe McGraw Hill vii Glencoe Geometry. NAME DATE PERIOD,1 Reading to Learn Mathematics,Vocabulary Builder continued. Vocabulary Term Definition Description Example,obtuse angle. perpendicular lines,PAHL ee gahn,right angle,segment bisector. supplementary angles,vertical angles,Glencoe McGraw Hill viii Glencoe Geometry.
NAME DATE PERIOD,1 1 Study Guide and Intervention,Points Lines and Planes. Name Points Lines and Planes In geometry a point is a location a line contains. points and a plane is a flat surface that contains points and lines If points are on the same. line they are collinear If points on are the same plane they are coplanar. Example Use the figure to name each of the following A D. a a line containing point A B, The line can be named as Also any two of the three N. points on the line can be used to name it,Lesson 1 1. b a plane containing point D, The plane can be named as plane N or can be named using three. noncollinear points in the plane such as plane ABD plane ACD and so on. Refer to the figure D,1 Name a line that contains point A.
2 What is another name for line m,3 Name a point not on. 4 Name the intersection of,5 Name a point not on line or line m. Draw and label a plane Q for each relationship,is in plane Q X. ST intersects AB,8 Point X is collinear with points A and P. 9 Point Y is not collinear with points T and P,10 Line contains points X and Y.
Glencoe McGraw Hill 1 Glencoe Geometry,NAME DATE PERIOD. 1 1 Study Guide and Intervention continued,Points Lines and Planes. Points Lines and Planes in Space Space is a boundless three dimensional set of. all points It contains lines and planes,a How many planes appear in the figure N. There are three planes plane N plane O and plane P B. b Are points A B and D coplanar,Yes They are contained in plane O. Refer to the figure,1 Name a line that is not contained in plane N B.
2 Name a plane that contains point B N D,3 Name three collinear points. Refer to the figure A B,4 How many planes are shown in the figure. 5 Are points B E G and H coplanar Explain,6 Name a point coplanar with D C and E. Draw and label a figure for each relationship,7 Planes M andN intersect in. 8 Line r is in plane N line s is in plane M and lines r and s J. intersect at point J r, 9 Line t contains point H and line t does not lie in plane M or.
Glencoe McGraw Hill 2 Glencoe Geometry,NAME DATE PERIOD. 1 1 Skills Practice,Points Lines and Planes,Refer to the figure. 1 Name a line that contains point D D p,2 Name a point contained in line n. 3 What is another name for line p,Lesson 1 1,4 Name the plane containing lines n and p. Draw and label a figure for each relationship,5 Point K lies on.
RT 6 Plane J contains line s, lies in plane B and contains 8 Lines q and f intersect at point Z. point C but does not contain point H in plane U,Refer to the figure F. 9 How many planes are shown in the figure E,10 How many of the planes contain points F and E. 11 Name four points that are coplanar,12 Are points A B and C coplanar Explain. Glencoe McGraw Hill 3 Glencoe Geometry,NAME DATE PERIOD.
1 1 Practice,Points Lines and Planes,Refer to the figure j. 1 Name a line that contains points T and P P Q, 2 Name a line that intersects the plane containing. points Q N and P,3 Name the plane that contains,Draw and label a figure for each relationship. intersect at point M 5 A line contains L 4 4 and M 2 3 Line. in plane T q is in the same coordinate plane but does. not intersect LM,Line q contains point N,Refer to the figure T Q. 6 How many planes are shown in the figure,7 Name three collinear points R.
8 Are points N R S and W coplanar Explain, VISUALIZATION Name the geometric term s modeled by each object. 9 10 tip of pin 11,12 a car antenna 13 a library card. Glencoe McGraw Hill 4 Glencoe Geometry,NAME DATE PERIOD. 1 1 Reading to Learn Mathematics,Points Lines and Planes. Pre Activity Why do chairs sometimes wobble, Read the introduction to Lesson 1 1 at the top of page 6 in your textbook.
Find three pencils of different lengths and hold them upright on your. desk so that the three pencil points do not lie along a single line Can you. place a flat sheet of paper or cardboard so that it touches all three pencil. How many ways can you do this if you keep the pencil points in the same. Lesson 1 1, How will your answer change if there are four pencil points. Reading the Lesson,1 Complete each sentence, a Points that lie on the same lie are called points. b Points that do not lie in the same plane are called points. c There is exactly one through any two points, d There is exactly one through any three noncollinear points. 2 Refer to the figure at the right Indicate whether each. statement is true or false D,a Points A B and C are collinear P. b The intersection of plane ABC and line m is point P A. c Line and line m do not intersect m,d Points A P and B can be used to name plane U.
e Line lies in plane ACB, 3 Complete the figure at the right to show the following. relationship Lines m and n are coplanar and lie in P n. plane Q Lines and m intersect at point P Line n, intersects line m at R but does not intersect line R. Helping You Remember, 4 Recall or look in a dictionary to find the meaning of the prefix co What does this prefix. mean How can it help you remember the meaning of collinear. Glencoe McGraw Hill 5 Glencoe Geometry,NAME DATE PERIOD. 1 1 Enrichment,Points and Lines on a Matrix, A matrix is a rectangular array of rows and columns Points and.
lines on a matrix are not defined in the same way as in Euclidean. geometry A point on a matrix is a dot which can be small or. large A line on a matrix is a path of dots that line up Between. two points on a line there may or may not be other points Three. examples of lines are shown at the upper right The broad line can. be thought of as a single line or as two narrow lines side by side. Dot matrix printers for computers used dots to form characters. The dots are often called pixels The matrix at the right shows. how a dot matrix printer might print the letter P, Draw points on each matrix to create the given figures. 1 Draw two intersecting lines that have 2 Draw two lines that cross but have. four points in common no common points, 3 Make the number 0 zero so that it 4 Make the capital letter O so that it. extends to the top and bottom sides extends to each side of the matrix. of the matrix, 5 Using separate grid paper make dot designs for several other letters Which were the. easiest and which were the most difficult,Glencoe McGraw Hill 6 Glencoe Geometry. NAME DATE PERIOD,1 2 Study Guide and Intervention,Linear Measure and Precision.
Measure Line Segments A part of a line between two endpoints is called a line. segment The lengths of M N and R,are written as MN and RS When you measure a. segment the precision of the measurement is half of the smallest unit on the ruler. Example 1 Example 2,Find the length of M S,Find the length of R. cm 1 2 3 4 in 1 2, The long marks are centimeters and the The long marks are inches and the short. shorter marks are millimeters The length of S,marks are quarter inches The length of R. M is 3 4 centimeters The measurement is 3,is about 1 inches The measurement is.
accurate to within 0 5 millimeter so M is 4, between 3 35 centimeters and 3 45 accurate to within one half of a quarter inch. centimeters long S,or inch so R is between 1 inches and. 1 inches long,Lesson 1 2,Find the length of each line segment or object. 1 A B 2 S T,cm 1 2 3 in 1,in 1 2 cm 1 2 3,Find the precision for each measurement. 5 10 in 6 32 mm 7 44 cm,8 2 ft 9 3 5 mm 10 2 yd,Glencoe McGraw Hill 7 Glencoe Geometry.
NAME DATE PERIOD,1 2 Study Guide and Intervention continued. Linear Measure and Precision,Calculate Measures On. PQ to say that point M is, between points P and Q means P Q and M are collinear M Q. and PM MQ PQ P,AC AB BC 3 cm We can say that the segments are B. congruent or A B,B C Slashes on the figure indicate which.
segments are congruent,Example 1 Find EF Example 2 Find x and AC. 1 2 cm 1 9 cm 2x 5,E D F A x B 2x C, Calculate EF by adding ED and DF B is between A and C. ED DF EF AB BC AC,1 2 1 9 EF x 2x 2x 5,3 1 EF 3x 2x 5. Therefore E is 3 1 centimeters long x 5,AC 2x 5 2 5 5 15. Find the measurement of each segment Assume that the art is not drawn to scale. 2 0 cm 2 5 cm 2 B,R S T A 2 43 in B C,X Y Z W X Y,Find x and RS if S is between R and T.
5 RS 5x ST 3x and RT 48 6 RS 2x ST 5x 4 and RT 32,7 RS 6x ST 12 and RT 72 8 RS 4x R. T and RT 24, Use the figures to determine whether each pair of segments is congruent. A 11 cm D X,Glencoe McGraw Hill 8 Glencoe Geometry. NAME DATE PERIOD,1 2 Skills Practice,Linear Measure and Precision. Find the length of each line segment or object,cm 1 2 3 4 5.
Find the precision for each measurement,3 40 feet 4 12 centimeters 5 9 inches. Lesson 1 2,Find the measurement of each segment,1in 1 41 in 4 9 cm 5 2 cm F 9 7 mm G H. Q P N A B C 15 mm, Find the value of the variable and YZ if Y is between X and Z. 9 XY 5p YZ p and XY 25 10 XY 12 YZ 2g and XZ 28, 11 XY 4m YZ 3m and XZ 42 12 XY 2c 1 YZ 6c and XZ 81. Use the figures to determine whether each pair of segments is congruent. B 2m C P 9 ft,3m 3m 5 ft,M 10 yd 5 ft,E D 12 yd X W.
Glencoe McGraw Hill 9 Glencoe Geometry,NAME DATE PERIOD. 1 2 Practice,Linear Measure and Precision,Find the length of each line segment or object. in 1 2 cm 1 2 3 4 5,Find the precision for each measurement. 3 120 meters 4 7 inches 5 30 0 millimeters,Find the measurement of each segment. 18 4 cm 4 7 cm 2 83 in 1 41 in W X 89 6 cm Y,P Q S A C D 100 cm.
Find the value of the variable and KL if K is between J and L. 9 JK 6r KL 3r and JL 27 10 JK 2s KL s 2 and JL 5s 10. Use the figures to determine whether each pair of segments is congruent. T 2 ft S A,2 ft 3 ft 6x,3 ft W 12 9 in F E, 14 CARPENTRY Jorge used the figure at the right to make a pattern A. for a mosaic he plans to inlay on a tabletop Name all of the F B. congruent segments in the figure,Glencoe McGraw Hill 10 Glencoe Geometry. NAME DATE PERIOD,1 2 Reading to Learn Mathematics,Linear Measure and Precision. Pre Activity Why are units of measure important, Read the introduction to Lesson 1 2 at the top of page 13 in your textbook. The basic unit of length in the metric system is the meter How many. meters are there in one kilometer, Do you think it would be easier to learn the relationships between the.
different units of length in the customary system used in the United. States or in the metric system Explain your answer. Reading the Lesson, 1 Explain the difference between a line and a line segment and why one of these can be. measured while the other cannot,Lesson 1 2, 2 What is the smallest length marked on a 12 inch ruler. What is the smallest length marked on a centimeter ruler. 3 Find the precision of each measurement, 4 Refer to the figure at the right Which one of the following A. statements is true Explain your answer D,4 5 cm C 4 5 cm. 5 Suppose that S is a point on V, and S is not the same point as V or W Tell whether.
each of the following statements is always sometimes or never true. b S is between V and W,c VS VW SW,Helping You Remember. 6 A good way to remember terms used in mathematics is to relate them to everyday words. you know Give three words that are used outside of mathematics that can help you. remember that there are 100 centimeters in a meter. Glencoe McGraw Hill 11 Glencoe Geometry,NAME DATE PERIOD. 1 2 Enrichment,Points Equidistant from Segments, The distance from a point to a segment is zero if the point is on the. segment Otherwise it is the length of the shortest segment from the. point to the segment, A figure is a locus if it is the set of all points that satisfy. a set of conditions The locus of all points that are inch A B. from the segment AB is shown by two dashed segments. with semicircles at both ends, 1 Suppose A B C and D are four different points and consider the locus.
of all points x units from A and x units from C,D Use any unit you find. convenient The locus can take different forms Sketch at least three. possibilities List some of the things that seem to affect the form of. C D Y A C D B, 2 Conduct your own investigation of the locus of points. equidistant from two segments Describe your results o. Point K lies on RT 6 Plane J contains line s 7 YP lies in plane B and contains 8 Lines q and f intersect at point Z point C but does not contain point H in plane U Refer to the figure 9 How many planes are shown in the figure 10 How many of the planes contain points F and E 11 Name four points that are coplanar 12 Are points A B and C coplanar Explain A W B E C D F U q