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NameclassdateGeometry Unit 1 Practicee.Lesson 1-1GT1. Persevere in solving problems. Identify eachfigure. Then give all possible names for the figure.Pa.SST2. What is a correct name for this plane?QRWXZb.CBAA. plane XZRB. plane WZC. plane WXZD. plane Xc.D3. How many different rays are in the figure?Name them.mFWZYXd.HKL 2015 College Board. All rights reserved.P1SpringBoard Geometry, Unit 1 Practice

Nameclass4. How many different angles are in the figure?Name them.dateLesson 1-26. Use this diagram.XAYTBZDPWC5. Use appropriate tools strategically. Draweach figure.a. RSa. How many radii are shown? Name them.b. TVb. How many diameters are shown? Name them.c. WXc. How is a chord similar to a diameter? How is achord different from a diameter?d. plane T containing points D and Ed. Make use of structure. Suppose you have twodifferent diameters of a circle. What must betrue about the point where the diametersintersect?e. CDE 2015 College Board. All rights reserved.2SpringBoard Geometry, Unit 1 Practice

Nameclassdate10. Think about a chord of a circle and a radius of thesame circle.7. Two angles are complementary. They also have thesame measure. Which statement is correct?a. What two things do the chord and the radiushave in common?A. The two angles are obtuse.B. The two angles are acute.C. The two angles must be adjacent.D. The two angles cannot be adjacent.b. How are the chord and the radius different?8. Reason quantitatively. P and Q aresupplementary. The measure of P is 30 degreesmore than the measure of Q. What is themeasure of each angle?Lesson 2-111. Use inductive reasoning to determine the next twoterms in each sequence.a. 12, 17, 22, 27, . . .b. 12, 17, 27, 42, . . .c. 12, 17, 23, 30, . . .d. 12, 60, 300, 1500, . . .e. 1, 4, 9, 16, . . .9. This diagram shows lines PQ , RS, and TV . Howmany angles appear to be obtuse? Name them.S12. The fourth term of a sequence is 40. Write the firstfive terms of two different sequences that satisfythat condition.PMVNRT 2015 College Board. All rights reserved.Q3SpringBoard Geometry, Unit 1 Practice

Nameclassdate14. Which rule describes how to find the next term inthe sequence?13. Persevere in solving problems. Use this picturepattern.0, 3, 9, 21, 45, 93, . . .A. Multiply the previous term by 3.B. Add 3 to the previous term, and then multiplythe result by 3.C. Multiply the previous term by 2, and then add 3.D. Divide the previous term by 3, and then add 3.a. Draw the next two shapes in the pattern.15. Construct viable arguments. Explain how youknew that the rules you did not choose in Item 14were incorrect.b. What numbers represent the next three figuresin the pattern?Lesson 2-216. Use expressions for even integers to show that theproduct of two even integers is an even integer.c. Verbally describe the pattern of the sequence.17. Consider these true statements. All glass objects are breakable. All windshields are made of glass. Tonette’s car has a windshield.d. How many dots are added from the firstdiagram to the second? From the seconddiagram to the third? From the third to thefourth? Explain how to find the nth term.Based on deductive reasoning, which of thefollowing statements is not necessarily true?A. Tonette has a breakable object.B. Tonette has a glass object.C. All windshields are breakable objects.D. All breakable objects are glass. 2015 College Board. All rights reserved.4SpringBoard Geometry, Unit 1 Practice

NameclassdateLesson 3-118. Make use of structure. Use deductive reasoningto prove that x 5 5 is not in the solution set of theinequality 2x 1 1 , 7. Be sure to justify each stepin your proof.21. Make use of structure. In each statement, tellwhether each bold term is undefined or defined.a. An angle is formed by two rays that have acommon endpoint.19. During the first month of school, studentsrecorded each day on which they had a quiz inmath class. A student stated that there is a mathquiz every Tuesday morning. Is the student’sstatement a conjecture or a theorem? Explain.b. A line segment consists of two points and allthe points between them.c. A triangle is the union of three segments thatintersect at their endpoints.20. Reason abstractly. A student knows that (1) anytwo diameters in a circle bisect each other and (2)RS and TV are two different diameters in the samecircle. The student concludes that RS and TVbisect each other.d. If two lines intersect, then there is exactly oneplane that contains the two lines.a. Is this an example of inductive or deductivereasoning? Explain.b. Is the conclusion correct? Support your answer. 2015 College Board. All rights reserved.5SpringBoard Geometry, Unit 1 Practice

NameclassLesson 3-222. Model with mathematics. Complete this twocolumn proof by providing the reasons for eachstatement.3x 2 5527Given:2Prove: x 5 23StatementsReasons3x 2 552721. a.2. 3x 2 5 5 2143. 3x 5 294. x 5 232. b.3. c.4. d.1.date26. Reason abstractly. Write each statement inif-then form.a. The only time I wake up early is when I set myalarm clock.b. I eat breakfast at a restaurant only if it is aweekend.23. Suppose you are given that p 5 2q 1 1 and thatp 5 8. Which of the following statements canyou prove?c. An obtuse angle has a measure between 90 and 180 .A. p 1 1 5 2qB. p 1 q 5 9C. 2q 1 1 5 8D. p 1 8 5 q27. State or describe a counterexample for eachconditional statement.a. If x2 5 25, then x 5 5.24. Identify the property that justifies the statement:If 3x 5 221, then x 5 27.A. Addition Property of EqualityB. Distributive PropertyC. Division Property of Equalityb. If three points A, B, and C are collinear, thenB is between A and C.D. Transitive Property of Equality25. a. Write a geometric statement that does not useany defined terms in geometry.c. If a triangle is obtuse, then it cannot beisosceles.b. Write a geometric statement that does not useany undefined terms. 2015 College Board. All rights reserved.6SpringBoard Geometry, Unit 1 Practice

Nameclassdate32. Write the following biconditional statement as twoconditional statements:28. Suppose that this statement is true: If I wear bootsor a raincoat, then I carry an umbrella. Alsosuppose that the hypothesis of that statement istrue. Which statement must also be true?People have the same ZIP code if and only if theylive in the same neighborhood.A. I am wearing boots.B. I am not wearing a raincoat.C. I am not carrying an umbrella.D. I am carrying an umbrella.33. Make use of structure. Use this statement: If3x 5 0, then x fi 0.29. Write a true conditional statement that includes3x 1 1this hypothesis:5 2.8a. Is the statement true? Explain.30. Model with mathematics. Write a two-columnproof to prove that your conditional statement inItem 29 is true.Statements1.3x 1 15282. a.3. c.4. e.b. Write the converse of the statement, and explainwhether or not the converse is true.Reasons1. Given2. b.3. d.4. Division (or Multiplication)Property of Equalityc. Write the inverse of the statement, and explainwhether or not the inverse is true.Lesson 3-3d. Write the contrapositive of the statement, andexplain whether or not the contrapositive istrue.31. Write the inverse and the contrapositive of eachstatement.a. If it is raining, then I stay indoors.b. If I have a hammer, then I hammer in themorning. 2015 College Board. All rights reserved.7SpringBoard Geometry, Unit 1 Practice

Nameclass34. Which two forms of a conditional statement alwayshave the same truth value?date38. Attend to precision. Use the centimeter rulershown.a. statement and inverseWRb. inverse and contrapositive14c. converse and contrapositive1516171819202122232425262728a. What is the length of RW?d. converse and inverse35. Reason abstractly. Use this statement: If two linesform equal adjacent angles, then the lines areperpendicular. Then tell whether each statement isthe inverse, converse, or contrapositive of theoriginal statement.b. What number on the ruler represents themidpoint of RW?a. If two lines are not perpendicular, then they donot form equal adjacent angles.c. Suppose Q is a point on RW . If QW 5 12, whatare the possible coordinates of point Q?b. If two lines do not form equal adjacent angles,then they are not perpendicular.d. Suppose point T is between points R and W andRT 1 . What is the length of RT?5TW 2Lesson 4-139. Reason quantitatively. On a number line, thecoordinate of point A is negative and thecoordinate of point B is positive.36. Suppose point T is between points R and V on aline. If RT 5 6.3 units and RV 5 13.1 units, thenwhat is TV?a. When will the midpoint of AB be positive?a. 2.5 unitsb. 6.8 unitsc. 7.8 unitsb. When will the midpoint of AB be negative?d. 19.4 unitsc. When will the midpoint of AB be zero?37. Suppose P is between M and N.a. If MN 5 10, MP 5 x 2 1, and PN 5 x 1 1,what is the value of x?d. When will the distance from A to B be negative?b. If PM 5 2x 2 5, PN 5 6x, and MN 5 5x 1 4,what is the value of x? 2015 College Board. All rights reserved.8SpringBoard Geometry, Unit 1 Practice

NameclassdateLesson 5-140. Points P, M, and T are on a line and PT 2 PM 5MT. Which point is between the other two?Explain your answer.46. Which expression represents the distance betweenpoints (m, n) and (p, q)?Lesson 4-241. Make sense of problems. Suppose that PQ bisects MPN. What conclusion can you make?A.(m 2 n)2 1 ( p 2 q )2B.(m 1 p )2 1 (n 1 q )2C.(m 2 p)2 1 (n 2 q )2D.(m 2 p)2 1 (n 2 q )247. A segment has endpoints L(22, 7) and K(5, 23).What are the coordinates of the midpoint of LK ?42. Suppose AT bisects CAR. If m CAT 5 5x andm CAR 5 9x 1 7, what is m TAR ?48. Attend to precision. The coordinates of the verticesof a triangle are A(24, 6), B(4, 22), and C(26, 24).a. Find AB.43. Suppose two angles are supplementary. Whichof the following terms CANNOT describe bothangles?A. acuteB. adjacentb. Find BC.C. congruentD. vertical44. D and E are complementary. If m D 5 5x 1 3and m E 5 3x 2 1, what is x?c. Find AC.45. a. Attend to precision. Draw a single diagramto represent the statements shown.Obtuse angle PQR is bisected by QA. PQA is bisected by QB . BQA is bisected by QC . AQR is bisected by QD .d. Based on the lengths of the sides, what kind oftriangle is ABC ?49. The coordinates of the vertices of a triangle areD(5, 6), E(7, 5), and F(4, 3). Find the perimeter ofthe triangle.b. Suppose m PQR 5 128 . Find m AQR . 2015 College Board. All rights reserved.9SpringBoard Geometry, Unit 1 Practice

Nameclass54. Which expression represents the midpoint of theline segment with endpoints (x, y) and (p, q)?50. Model with mathematics. Every point on a circleis the same distance from the center of the circle. If(x, y) represents any point on a circle and (5, 2) isthe center of the circle, use the Distance Formula torepresent the length of the radius r of the circle. x 1 y p1q a. , 22 x 2 p y 2q b. , 22 Lesson 5-2 x 1 p y 1q C. , 22 51. Model with mathematics. BC has endpointsB(23, 25) and C(12, 12). Find the coordinates ofthe midpoint of BC.xp yqd. , 2 2 55. For the coordinates (5, 8) and (9, 14), one is anendpoint of a line segment and the other is themidpoint. How many possibilities are there forthe other endpoint? Find each one. Explainyour method.52. In the diagram shown, points S and T are themidpoints of PQ and PR, respectively.y108P(4, 7)6Lesson 6-1T422624dateS22256. Construct viable arguments. Use the diagramshown.R(10, 3)46810Ax22BQ(22, 23)241262a. Find the coordinates of points S and T.CTWrite a statement that can be justified by each ofthe following:a. definition of angle bisectorb. Find the length of ST .53. Construct viable arguments. Given: A(2, 5),B(0, 0), and C(4, 2).a. Find the coordinate of M, the midpoint of BC.b. Angle Addition Postulateb. Which of the points, B, M, or C, is closest to A? 2015 College Board. All rights reserved.10SpringBoard Geometry, Unit 1 Practice