Let s Get This Started!

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Patricia Osborne
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1 Lesson. Skills Practice Name Date Let s Get This Started! Points, Lines, Planes, Rays, and Line Segments Vocabulary Write the term that best completes each statement.. A geometric figure created without using tools is a(n).. are two or more lines that are not in the same plane. 3. A(n) is a location in space. 4. The points where a line segment begins and ends are the. 5. A(n) is a straight continuous arrangement of an infinite number of points. 6. Two or more line segments of equal measure are. 7. You a geometric figure when you use only a compass and straightedge. 8. Points that are all located on the same line are. 9. A(n) is a portion of a line that includes two points and all of the collinear points between the two points. 0. A flat surface is a(n).. A(n) is a portion of a line that begins with a single point and etends infinitely in one direction.. Two or more lines located in the same plane are. 3. When you a geometric figure, you use tools such as a ruler, straightedge, compass, or protractor. Chapter Skills Practice 345

2 Lesson. Skills Practice page Problem Set Identify the point(s), line(s), and plane(s) in each figure.. A C Points: A, B, and C Lines: AB and BC B Plane: m m. Z Y X a 3. p R Q S 4. M L N 346 Chapter Skills Practice

3 Lesson. Skills Practice page 3 Name Date Draw a figure for each description. Label all points mentioned in the description. 5. Points R, S, and T are collinear such that point T is located halfway between points S and R. S T R 6. Points A, D, and X are collinear such that point A is located halfway between points D and X. 7. Points A, B, and C are collinear such that point B is between points A and C and the distance between points A and B is twice the distance between points B and C. 8. Points F, G, and H are collinear such that point F is between points G and H and the distance between points F and G is one third the distance between points G and H. Identify all eamples of coplanar lines in each figure. 9. m p n q 0. a d c b Lines m and p are coplanar. Lines n and q are coplanar. Chapter Skills Practice 347

4 Lesson. Skills Practice page 4. z y w. s p t q r u Identify all skew lines in each figure g h a c f b Lines f and g are skew. Lines f and h are skew w n y m l 348 Chapter Skills Practice

5 Lesson. Skills Practice page 5 Name Date Draw and label an eample of each geometric figure. 7. XY 8. CD X Y 9. PR 0. FG. HM. KJ Chapter Skills Practice 349

6 Lesson. Skills Practice page 6 Use symbols to write the name of each geometric figure. 3. R T 4. A RT B 5. X 6. M N Y 7. C 8. S D R Use a ruler to measure each segment to the nearest centimeter. Then use symbols to epress the measure of each segment. 9. A B AB 5 4 centimeters or m AB 5 4 centimeters 30. A B 3. A B 3. A B 350 Chapter Skills Practice

7 Lesson. Skills Practice Name Date Attack of the Clones Translating and Constructing Line Segments Vocabulary Choose the term from the bo that best completes each statement. Distance Formula transformation pre-image rigid motion translation arc copying (duplicating) a line segment image. A(n) is a transformation of points in space.. The new figure created from a translation is called the. 3. A(n) is a part of a circle and can be thought of as the curve between two points on a circle. 4. A(n) is the mapping, or movement, of all the points of a figure in a plane according to a common operation. 5. The can be used to calculate the distance between two points on a coordinate place. 6. In a translation, the original figure is called the. 7. A(n) is a rigid motion that slides each point of a figure the same distance and direction. 8. A basic geometric construction called can be used to translate a line segment when measurement is not possible. Chapter Skills Practice 35

8 Lesson. Skills Practice page Problem Set Calculate the distance between each given pair of points. Round your answer to the nearest tenth, if necessary.. (3, ) and (6, 5) 5 3, y 5, 5 6, y 5 5 d 5 ( ) (y y ) d 5 (6 3 ) (5 ) d d d 5 5 d 5 5. (, 8) and (4, 3) 3. (6, 4) and (5, ) 4. (9, ) and (, 9) 5. (0, 6) and (8, 0) 6. (5, 8) and (, 9) 35 Chapter Skills Practice

9 Lesson. Skills Practice page 3 Name Date Calculate the distance between each given pair of points on the coordinate plane. Round your answer to the nearest tenth, if necessary. 7. y 5, y 5 8, 5 7, y 5 3 d 5 ( 8 ) (y y ) d 5 (7 ) (3 8 ) 6 d 5 5 (5) 4 d d d y Chapter Skills Practice 353

10 Lesson. Skills Practice page 4 9. y y Chapter Skills Practice

11 Lesson. Skills Practice page 5 Name Date. y y Chapter Skills Practice 355

12 Lesson. Skills Practice page 6 Translate each given line segment on the coordinate plane as described. 3. Translate AB 8 units to the left. y 4. Translate CD 9 units down. y A9 8 6 A 8 6 C D 4 4 B9 B Translate EF 7 units to the right. y 6. Translate GH units up. y E G F H 356 Chapter Skills Practice

13 Lesson. Skills Practice page 7 Name Date 7. Translate JK units down and 7 units to the left. y 8. Translate MN 5 units down and 0 units to the right. y 8 J K M N Construct each line segment described. 9. Duplicate AB. 0. Duplicate CD. A B C D A9 B9. Duplicate EF.. Duplicate GH. E F G H Chapter Skills Practice 357

14 Lesson. Skills Practice page 8 3. Construct a line segment twice the length of JK. J K 4. Construct a line segment twice the length of MN. M N 358 Chapter Skills Practice

15 Lesson.3 Skills Practice Name Date Stuck in the Middle Midpoints and Bisectors Vocabulary Match each definition to the corresponding term.. midpoint a. a line, line segment, or ray that divides a line segment into two line segments of equal measure. Midpoint Formula b. a basic geometric construction used to locate the midpoint of a line segment 3. segment bisector c. a point eactly halfway between the endpoints of a line segment 4. bisecting a line segment d. (, y y ) Problem Set Determine the midpoint of a line segment with each set of given endpoints.. (8, 0) and (4, 6). (3, 8) and (9, 0) 5 8, y , y 5 6 (, 6, y y ) 5 ( 8 4, 0 6 ) 5 ( ) 5 (6, 3) Chapter Skills Practice 359

16 Lesson.3 Skills Practice page 3. (7, ) and (3, 6) 4. (6, 3) and (4, 5) 5. (0, ) and (0, 4) 6. (, 7) and (8, 9) Determine the midpoint of the given line segment on each coordinate plane using the Midpoint Formula. 7. y 5 3, y , y 5 8 (, y y ) 5 ( 3 7, 8 ) 5 ( 0, 0 ) 5 (5, 5) Chapter Skills Practice

17 Lesson.3 Skills Practice page 3 Name Date 8. y y Chapter Skills Practice 36

18 Lesson.3 Skills Practice page 4 0. y y Chapter Skills Practice

19 Lesson.3 Skills Practice page 5 Name Date. y Locate the midpoint of each line segment using construction tools and label it point M. 3. A M B Chapter Skills Practice 363

20 Lesson.3 Skills Practice page 6 4. C D 5. E F 364 Chapter Skills Practice

21 Lesson.3 Skills Practice page 7 Name Date 6. G H 7. K J Chapter Skills Practice 365

22 Lesson.3 Skills Practice page 8 8. Q P 366 Chapter Skills Practice

23 Lesson.4 Skills Practice Name Date What s Your Angle? Translating and Constructing Angles and Angle Bisectors Vocabulary Define each term in your own words.. angle. angle bisector Describe how to perform each construction in your own words. 3. copying or duplicating an angle 4. bisecting an angle Chapter Skills Practice 367

24 Lesson.4 Skills Practice page Problem Set Translate each given angle on the coordinate plane as described.. Translate /ABC 9 units to the left. y. Translate /DEF units down. y A9 8 A D B9 4 C9 B C E F Translate /GHJ 0 units to the right. y 4. Translate /KLM 3 units up. y H 4 6 G J K 4 6 L 8 M Chapter Skills Practice

25 Lesson.4 Skills Practice page 3 Name Date 5. Translate /NPQ 8 units to the left and units down. y 6. Translate /RST 5 units to the left and 9 units up. y P N Q R T S 8 8 Construct each angle as described. 7. Copy /B. 8. Copy /D. C B D D S R T /CBD > /SRT Chapter Skills Practice 369

26 Lesson.4 Skills Practice page 4 9. Copy /P. 0. Copy /Z. P Z. Construct an angle that is twice the measure of /K. K 370 Chapter Skills Practice

27 Lesson.4 Skills Practice page 5 Name Date. Construct an angle that is twice the measure of /M. M Construct the angle bisector of each given angle. 3. A 4. D P B PD is the angle bisector of /P. B S X Chapter Skills Practice 37

28 Lesson.4 Skills Practice page 6 7. Construct an angle that is one-fourth the measure of /F. F 8. Construct an angle that is one-fourth the measure of /X. X 37 Chapter Skills Practice

29 Lesson.5 Skills Practice Name Date If You Build It... Constructing Perpendicular Lines, Parallel Lines, and Polygons Problem Set Construct a line perpendicular to each given line and through the given point.. Construct a line that is perpendicular to CD and passes through point T. C T D. Construct a line that is perpendicular to AB and passes through point X. A X B Chapter Skills Practice 373

30 Lesson.5 Skills Practice page 3. Construct a line that is perpendicular to RS and passes through point W. R W S 4. Construct a line that is perpendicular to YZ and passes through point G. Y Z G 374 Chapter Skills Practice

31 Lesson.5 Skills Practice page 3 Name Date 5. Construct a line that is perpendicular to MN and passes through point J. J N M 6. Construct a line that is perpendicular to PQ and passes through point R. P R Q Chapter Skills Practice 375

32 Lesson.5 Skills Practice page 4 Construct a line parallel to each given line and through the given point. 7. Construct a line that is parallel to AB and passes through point C. C q A B Line q is parallel to AB. 8. Construct a line that is parallel to DE and passes through point F. D E F 376 Chapter Skills Practice

33 Lesson.5 Skills Practice page 5 Name Date 9. Construct a line that is parallel to GH and passes through point J. G J H 0. Construct a line that is parallel to KL and passes through point M. K M L Chapter Skills Practice 377

34 Lesson.5 Skills Practice page 6. Construct a line that is parallel to NP and passes through point Q. N Q P. Construct a line that is parallel to RT and passes through point W. R W T 378 Chapter Skills Practice

35 Lesson.5 Skills Practice page 7 Name Date Construct each geometric figure. 3. Construct an equilateral triangle. The length of one side is given. 4. Construct an equilateral triangle. The length of one side is given. Chapter Skills Practice 379

36 Lesson.5 Skills Practice page 8 5. Construct an isosceles triangle that is not an equilateral triangle such that each leg is longer than the base. The length of the base is given. 6. Construct an isosceles triangle that is not an equilateral triangle such that each leg is shorter than the base. The length of the base is given. 380 Chapter Skills Practice

37 Lesson.5 Skills Practice page 9 Name Date 7. Construct a square. The perimeter of the square is given. 8. Construct a square. The perimeter of the square is given. Chapter Skills Practice 38

38 Lesson.5 Skills Practice page 0 9. Construct a rectangle that is not a square. The perimeter of the rectangle is given. 0. Construct a rectangle that is not a square. The perimeter of the rectangle is given. 38 Chapter Skills Practice

39 Lesson.6 Skills Practice Name Date What s the Point? Points of Concurrency Vocabulary Describe similarities and differences between each pair of terms.. concurrent and point of concurrency. incenter and orthocenter 3. centroid and circumcenter 4. altitude and median Chapter Skills Practice 383

40 Lesson.6 Skills Practice page Problem Set Draw the incenter of each triangle Draw the circumcenter of each triangle Chapter Skills Practice

41 Lesson.6 Skills Practice page 3 Name Date Draw the centroid of each triangle Chapter Skills Practice 385

42 Lesson.6 Skills Practice page Draw the orthocenter of each triangle Chapter Skills Practice

43 Lesson.6 Skills Practice page 5 Name Date Answer each question about points of concurrency. Draw an eample to illustrate your answer. 33. For which type of triangle are the incenter, circumcenter, centroid, and orthocenter the same point? equilateral triangles 34. For which type of triangle are the orthocenter and circumcenter outside of the triangle? 35. For which type of triangle are the circumcenter and orthocenter on the triangle? Chapter Skills Practice 387

44 Lesson.6 Skills Practice page For which type of triangle are the incenter, circumcenter, centroid, and orthocenter all inside the triangle? 37. For what type(s) of triangle(s) do the centroid, circumcenter, and orthocenter all lie on a straight line? 38. For what type of triangle is the orthocenter a verte of the triangle? 388 Chapter Skills Practice

45 Lesson.6 Skills Practice page 7 Name Date Given the coordinates of the vertices of a triangle, classify the triangle using algebra. 39. A(5, 5), B(5, 5), C(0, 5) segment AB segment AC segment BC d 5 [5 ( 5) ] (5 5 ) d 5 [0 (5) ] (5 5 ) d 5 (0 5 ) ( 5 5 ) d d 5 5 ( 0) d 5 00 d 5 5 d 5 5 d 5 0 d.8 d.8 The lengths of two of the segments are equal, so the triangle is isosceles. d 5 (5 ) (0 ) 40. R(3, ), S(, ), T(4, ) 4. F(, 5), G(, 6), H(5, 4) Chapter Skills Practice 389

46 Lesson.6 Skills Practice page 8 4. M(5, ), N(3, 5), P(, 3) 43. K(, ), L(4, 3), M(, 5) 390 Chapter Skills Practice

47 Lesson.6 Skills Practice page 9 Name Date 44. E(5, 7), F(3, 4), G(8, ) Chapter Skills Practice 39

48 39 Chapter Skills Practice

a triangle with all acute angles acute triangle angles that share a common side and vertex adjacent angles alternate exterior angles

acute triangle a triangle with all acute angles adjacent angles angles that share a common side and vertex alternate exterior angles two non-adjacent exterior angles on opposite sides of the transversal;