Chapter Review. Skills and Concepts. Vocabulary Review. Resources. Chapter Review. Chapter

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1 hapter hapter eview hapter eview Vocabulary eview acute angle (p. 37) adjacent angles (p. 38) angle (p. 36) angle bisector (p. 6) axiom (p. 8) collinear points (p. 7) compass (p. ) complementary angles (p. 38) congruent angles (p. 37) congruent segments (p. 3) conjecture (p. 5) construction (p. ) coordinate (p. 3) coplanar (p. 7) School.com or: Vocabulary quiz Web ode: auf-05 Skills and oncepts counterexample (p. 5) foundation drawing (p. ) inductive reasoning (p. ) isometric drawing (p. 0) line (p. 7) midpoint (p. 3) net (p. ) obtuse angle (p. 37) opposite rays (p. 3) orthographic drawing (p. ) parallel lines (p. ) parallel planes (p. ) perpendicular bisector (p. 5) perpendicular lines (p. 5) hoose the correct term to complete each sentence.. igures that are in the same plane are 9. coplanar plane (p. 7) point (p. 7) postulate (p. 8) ray (p. 3) right angle (p. 37) segment (p. 3) skew lines (p. ) space (p. 7) straight angle (p. 37) straightedge (p. ) supplementary angles (p. 38) vertical angles (p. 38). (n) 9 is the part of a line consisting of two endpoints and all points between them. segment 3. Two segments with the same length are 9. congruent. (n) 9 of a segment is a point that divides the segment into two congruent segments. midpoint 5. angle bisector 5. (n) 9 is a ray that divides an angle into two congruent angles. 6. conclusion based upon inductive reasoning is sometimes called a(n) 9. conjecture 7. (n) 9 is an accepted statement of fact. postulate or axiom 8. 9 are coplanar lines that do not intersect. arallel lines 9. (n) 9 is an angle whose measure is between 90 and 80. obtuse angle esources Student dition xtra Skills, Word roblems, roof ractice, h. 7, p. 78 nglish/spanish lossary, p. 779 ostulates and Theorems, p. 770 Table of Symbols, p. 763 Vocabulary and Study Skills worksheet Spanish Vocabulary and Study Skills worksheet Interactive Textbook udio lossary Online Vocabulary uiz Spanish Vocabulary/Study Skills Vocabulary/Study Skills Name lass ate : Vocabulary or use with hapter eview LL - Objectives To use inductive reasoning to make conjectures You use inductive reasoning when you make conclusions based on patterns you observe. conjecture describes a conclusion reached using inductive reasoning. counterexample to a conjecture is an example for which the conjecture is incorrect. ind a pattern for each sequence. escribe the pattern and use it to show the next two terms See margin. Study Skill: Many words in nglish have more than one meaning. Often a word has one meaning in ordinary conversation, and a different specific meaning or exact definition when it is used in math or science or grammar. You can often figure out which meaning to use by looking at the sentence that contains the word. To help you decide what a word means, consider the surroundings, or context, in which you see the word. ead the mathematical definition in the left column and the sentence in the right column. In the blank in the middle, write the one word from the list below that fits both the definition and the sentence. The first one is done for you. base like origin constant natural power element open real term efinition Sentence real. kind of number in a set of It is a event. rational and irrational It actually happened. numbers together 0. 0, 35, 30, 5, c. 5, 5, 5, 5, c. 3, 7, 0, 3, 6, c. a term that has no variable That noise is. It just never seems to stop. 3. a number that is multiplied ut this statue on its repeatedly so it will not fall over ,, 96, 38, c.,, 8, 6, 3, c 5.,, 5, 6, 9, c 6. raw the next figure in the sequence. See left.. the kind of terms that have I really that kind exactly the same variable of food. It is my favorite. factors 5. the kind of math sentence The door should be that has one or more variables so the customers can come in. 6. the base and exponent of an Turn off the expression of the form a n before you try to repair those wires. 7. the kind of number you Let s go for a walk by the lake. might use to count rocks I want to enjoy the or pencils world. 8. the point where the axes of What is the of a coordinate plane intersect that custom? I wonder how it began. earson ducation, Inc. ll rights reserved. hapter hapter eview 7 9. a number, a variable, or the e will come home from product of a number and one college at the end of the or more variables. 0. the name of each item in a One in water is matrix oxygen. hydrogen. The other is eading and Math Literacy Masters lgebra 0. subtract 5; 0, 5. nswers may vary. Sample: mult. by ; 5, 5. subtr.7;, 8 3. mult. by ; 536, 6. mult. by ; 6, 8 5. alternate adding and 3; 0, 3 7

2 Objectives net is a two-dimensional pattern that you can fold to form a three-dimensional figure. net shows all surfaces of a figure in one view. To make isometric and orthographic drawings To draw nets for threedimensional figures 7. The net at the right is for a number cube. What are the three sums of the numbers on opposite surfaces of the cube?, 6, 8. On another number cube, the numbers on each pair of opposite surfaces add to 7. raw a net for this number cube. See margin and - Objectives oints that lie on the same line are collinear points. oints and lines in the same plane are coplanar. Segments and rays are parts of lines. To understand basic terms and postulates of geometry To identify segments and rays To recognize parallel lines Lines that are coplanar and do not intersect are parallel lines. Lines in space that are not parallel and do not intersect are skew. lanes that do not intersect are parallel planes. Use the figure at the right for xercises Name two intersecting lines. and 9. nswers may vary. Samples are given. T S. T and S 3. always 0. Name three noncollinear points.,,. Name a pair of parallel planes.. Name three lines that intersect at.,t, omplete with always, sometimes, or never to make a true statement. sometimes 3. line and a point are 9 coplanar.. Two segments are 9 coplanar. 5. Skew lines are 9 coplanar. never 6. Two points are 9 collinear. always -5 and -6 Objectives To find the lengths of segments To find the measures of angles To identify special angle pairs Segments with the same length are congruent segments. midpoint of a segment divides the segment into two congruent segments. Two rays with the same endpoint form an angle. ngles can be classified as acute, right, obtuse, or straight. ngles with the same measure are congruent angles. 7. ind two possible coordinates of so that = 5. 7, 3 8. ind the coordinate of the midpoint of x lgebra ind the value of each variable. 9. 3m + 5 m (3x 3) (x 6) 3. nswers may vary. Samples are given. a. /, / b. /, / c. /, / 3. Name a pair of each of the following. a. complementary angles b. supplementary angles c. vertical angles 7 hapter hapter eview 7

3 -7 Objectives To use a compass and a straightedge to construct congruent segments and congruent angles To use a compass and a straightedge to bisect segments and angles onstruction is the process of making geometric figures using a compass and a straightedge. our basic constructions involve constructing congruent segments, congruent angles, and bisectors of segments and angles. erpendicular lines intersect at right angles. perpendicular bisector of a segment is perpendicular to the segment at its midpoint, and bisects it into two congruent segments. n angle bisector is a ray that divides an angle into two congruent angles. 3. Use a protractor to draw a 68 angle. Then construct an angle congruent to your 68 angle. See margin. 33. Use a ruler and draw. a. onstruct >. a b. See margin. b. onstruct the perpendicular bisector of. earson ducation, Inc. ll rights reserved. lternative ssessment Name lass ate lternative ssessment orm hapter Use a straightedge and compass for all four tasks. TS a. xplain in detail the patterns you observe in igures,, and 3. b. iven those patterns, draw igure. Is there more than one possible answer for igure? xplain. c. What would igure 5 look like? escribe.?? igure igure igure 3 igure TS a. raw and label a figure that fits * the ) following * description: ) lane contains parallel lines and. intersects at point, but and are not in plane. ngles,, and are three different right angles. b. an you name three noncoplanar points in your figure? xplain. c. Name three points that are not collinear. L -8 Objectives To find the distance between two points in the coordinate plane To find the coordinates of the midpoint of a segment in the coordinate plane The x-axis and the y-axis intersect at the origin (0, 0) and determine a coordinate plane. You can find the coordinates of the midpoint M of with endpoints (x, y ) and (x, y ) using the Midpoint ormula. M = a x x, y y b You can find the distance d between points (x, y ) and (x, y ) using the istance ormula. d = #x x y y ind the distance between the points to the nearest tenth. 3. (-, 5), (0, ) 35. (-, -), (6, ) 36. (-7, 0), (5, 8). units 7.6 units. units has endpoints ( 3, ) and (3, ). 37. ind the coordinates of the midpoint of. (0, 0) 38. ind to the nearest tenth. 7. units eometry hapter orm Test a b. -9 Objectives To find perimeters of rectangles and squares, and circumferences of circles To find areas of rectangles, squares, and circles The perimeter of a polygon is the sum of the lengths of its sides. The area of a polygon is the number of square units it encloses. ormulas: Square ectangle ircle = s = b + h = pd or = pr = s = bh = pr ind the perimeter and the area of each figure ft 8 cm 3 ft 3 in. 3 cm 38 ft 5 in. 3 in. 6 cm 78 ft 0 in. ind the circumference and the area of each circle to the nearest hundredth.. r = 3 in. 3. d = 5 m. r = 6 m N 8.85 in. N 7. m, N m, N 3.7 m N 8.7 in. N 76.7 m hapter hapter eview 73 73

4 hapter hapter Test hapter Test School.com or: hapter Test Web ode: aua-05 h. Test L dapted h. Test L h. lternative ssessment Spanish h. Test L Spanish h. lternative ssessment L Informal eometry h. Test, orms & xamview -OM h. re-made Test Make your own h. test Online hapter Test at dapted hapter Test hapter Test earson ducation, Inc. ll rights reserved. Name lass ate hapter Test hapter escribe each pattern, and find the next two terms or drawings in each sequence..,7,,7,.... -,, -,, ,,6,, ritical Thinking Make a conjecture about the relationship between three consecutive whole numbers based on this relationship illustrated by the numbers 3,, and 5: (3 5) = -. an you find a counterexample? Use the figure to answer xercises Name three collinear points. 7. Name four coplanar points. 8. Name four noncoplanar points. 9. ind each intersection. a. * ) and plane b. * ) and plane c. and * ) d. plane and point Use the figure to answer xercises Name a line parallel to.. Name two lines skew to.. Name a pair of parallel planes. 3. Name two intersecting planes.. lgebra M = 6. Use the figure to find each of the following. a. x x 3x 7 b. M M c. 5. rror nalysis Show that the conjecture below is false by finding a counterexample. If two lines do not intersect, then they are not coplanar lines. orm eometry hapter orm Test 7 O L escribe each pattern and find the next two terms of each sequence. 3. See margin.. 8, -,, -, c. 0,,, 6, 8, c 3. S. Open-nded Write two different sequences whose first three terms are,,. escribe each pattern. See margin. 5. raw a net for a cube. See margin. Use the figure for xercises Name three collinear points.,, 7. Name four coplanar points. Sample:,,, 8. What is the intersection of and plane? 9. ow many planes contain each line and each point? a. and point b. and point c. and point d. and point 9b. infinitely many 0. Track The running track is a rectangle with a half circle on each end. If I and are diameters, find the area inside the track to the nearest tenth. ft 9,05.0 ft omplete with always, sometimes, or never to make each statement ) ) true.. L and T are 9 opposite rays. never. our points are 9 coplanar. sometimes 3. Skew lines are 9 coplanar. never. Two segments that lie in parallel lines are 9 parallel. always 5. The intersection of two planes is 9 a point. never 7 hapter hapter Test I 00 ft * ) x x x 6. lgebra = 8. ind the value of x. 0 x 5 x 3 7. lgebra M(x, y) is the midpoint of with endpoints (5, 9) and (7, 9). a. ind the values of x and y. (, 9) b. Show M = M. M M "36 8. To the nearest tenth, find the perimeter of n with vertices (-, -), (0, 5), and (3, -). 9. units or the given dimensions, find the area of each figure to the nearest hundredth. 9. rectangle 0. square. circle b = m s = 3.5 in. d = 9 cm h = cm.5 in cm 800 cm or 0.08 m lgebra Use the figure for xercises. In xercises and 3, find the value of each variable.. m& = 3x +, m& = 5x m& = 7y +, m& = y Name two complementary angles. nswers may vary. Sample: &, & 5. Writing Why is it useful to have more than one way of naming an angle? See margin, p raw an obtuse &. Use a compass and straightedge to bisect the angle. See margin, p. 75. Use the figure to complete xercises VW is the 9 of Y. # bisector V 8. If Y = 3.5, then Y = = Y is the midpoint of 9. W Y ; Y 3. arpeting ow many square yards of carpet are needed to carpet a room that is 5 ft long and 0 ft wide? 333 yd hapter Test. iv. each preceding term by ;,. dd to the preceding term; 0, 7 3. otate the U clockwise one-quarter turn. lphabet is backwards; O N. nswers may vary. Sample:,,, 8, 6, 3,...,,, 7,, 6,... In the first seq. double each term. In the second seq., add consecutive counting numbers. 5.

5 Standardized Test rep IN OMNSION Standardized Test rep eading omprehension ead the passage below, then answer the questions on the basis of what is stated or implied in the passage. Instructions for uilding the ainbow Toy hest 3 Use -in.-thick plywood. ut the top and bottom 8 in. by in. aint the top red and the bottom violet. Use -in.-thick plywood. ut the two sides 8 in. by 60 in. aint: left side brown, right side white. ut the three shelves 5 in. by in. aint: top orange, middle yellow, bottom green. ut the two dividers in. by 5 in. aint: left blue, right indigo. Use particleboard. ut the back in. by 60 in. aint the back gray. ssemble the painted pieces using nails and glue. Students must be able to extract information from reading passages, answer multiple-choice questions, and construct responses in order to be successful on current state and national assessments. To answer the questions, students apply skills and concepts from this chapter and previous chapters. Multiple hoice: Items 8 ree esponse: Items 9 esources Test rep Workbook rab & o umulative eview xamview -OM Standardized Test ractice. ow many pieces must be cut to make the chest? What is the shape of each piece? square rectangular round cannot be determined 3. Which uses thicker wood, a divider or the top? divider top same thickness cannot be determined ssume that the toy chest has been assembled.. Take the top of the bookshelf as the first horizontal surface and count downward. What is the color of the fourth surface down? white yellow green blue 5. Which corners are NOT coplanar? the four corners of the right side the two top corners of the left side and the two front corners of the bottom the two top corners of the right side and the two bottom corners of the left side the two front corners of the top and the two back corners of the bottom 6. Where do the violet board and the particleboard meet? the front edge of the violet board the back edge of the left side the right edge of the bottom the bottom edge of the back 7. Which edge is skew to the front edge of the orange board? the left edge of the orange board the top edge of the white board the back edge of the yellow board the front edge of the middle shelf 8. What are the colors of two boards that are NOT perpendicular? blue and gray indigo and violet blue and white yellow and brown 9. ow tall is the toy chest? 6 in. 0. What is the area of the top? 756 in.. What is the perimeter of the front? 07 in.. The back edge of each shelf touches the back of the chest. ow far recessed is the front edge of a shelf from the front edge of a side? in. Spanish ssessment esources Spanish umulative eview Spanish umulative eview umulative eview earson ducation, Inc. ll rights reserved. Name lass ate umulative eview hapter or xercises 3, choose the correct letter.. ind a pattern for the sequence. Use the pattern to show the next term., 3, 9, 7, c If XY =, what is the measure of XZ? x 3x X Y Z If =, find the value of y. 3y 5y ind a pattern for the sequence. Use the pattern to show the next term. S, M, T, W, c. S.. M. T Use the figure at the right for xercises What * is ) the intersection of plane I and plane I?.. point. * ). I 6. Which four points are coplanar?.,,, I.,,,.,,,.,, I, 7. What is another way to name plane?. point. * ). plane. plane I 8. What is the intersection of * ) and plane?.. point. * ). point 9. ind the value of x (x 5) (8x) S T I LL hapter Standardized Test rep 75 ) 0. OM is the 9 of &LON.. perpendicular bisector. midpoint. segment bisector. angle bisector O L M N eometry hapter umulative eview nswers may vary. Sample: Some ways of naming an l can help identify a side or vertex

Segments, Rays, Parallel Lines and Planes Q L R M. Segment AB. Endpoint. Ray YX. Naming Segments and Rays

Segments, Rays, Parallel Lines and Planes Q L R M. Segment AB. Endpoint. Ray YX. Naming Segments and Rays - egments, ays, arallel ines and lanes -. lan What You ll earn To identify segments and rays To recognize parallel lines... nd Why To identify compass directions that can be represented by opposite rays,