Name Class Date Geometry Unit 2 Practice
NameclassdateGeometry Unit 2 PracticeLesson 9-11. Which of the following shows the rectangle on the grid under the transformation (x, y) (x 2 1, y 1 0x525x2525210 2015 College Board. All rights reserved.1SpringBoard Geometry, Unit 2 Practice
Nameclassdate2. What function describes the transformation shown? Write your answer as (x, y) (?, ?).yy55525x52525x255. A rectangle on a coordinate plane has side lengthsof 5 units and 4 units, so its diagonal is 41 units.The position of the rectangle is changed by a rigidtransformation.a. What is the length of the diagonal of thetransformed rectangle?3. Express regularity with repeated reasoning.One of the vertices of a rectangle is (23, 24).What is the image of that vertex after eachtransformation?a. (x, y) (x, y 1 7)b. (x, y) (x 2 3, y 1 2)b. Explain your answer to Part a.c. (x, y) (2x, y 2 5)Lesson 9-26. Model with mathematics. Use the diagramshown.d. (x, y) (2y, 2x)4. Reason quantitatively. Label each transformationas rigid or nonrigid.IIa. (x, y) (x 1 7, y 1 3)Ib. (x, y) (x 1 1, 2y)IVIIIc. (x, y) (2x, 2y)d. (x, y) (2x, 2y 21)Which pair of figures can represent the pre-imageand image in a translation?A. I and IVB. II and IIIe. (x, y) (x 1 5, 0)C. III and IV 2015 College Board. All rights reserved.2D. I and IIISpringBoard Geometry, Unit 2 Practice
Nameclass7. Use the diagram shown.10. Make sense of problems. In the diagram shown,two of the triangles represent the translation(x, y) (x 2 4, y 1 5).yAdate5By5525xCBC525xA2525a. What is the image of point A under thetranslation (x, y) (x 2 3, y 2 2)?a. Which figure is the pre-image in the translation?b. What translation maps point B to (0, 0)? Writeyour answer as a function (x, y) (?, ?).b. Which figure is the image in the translation?8. Line segment PQ has endpoints P(3, 22) andQ(2, 4). The translation (x, y) (x 2 3, y 1 5)maps PQ to RS .c. Explain your answers to Parts a and b.d. What translation will take the image back to thepre-image? Write your answer as a function(x, y) (?, ?).a. What is the relationship between PQ and RS ?b. What are the coordinates of the endpoints of RS ?Lesson 9-311. A point is located at (24, 3). Which reflectionmaps that point to (10, 3)?9. Consider the point (26, 3).a. What is the image of (26, 3) under thetranslation (x, y) (x 1 5, y 2 3)?A. a reflection across the line x 5 3B. a reflection across the line x 5 7C. a reflection across the line x 5 10b. What translation takes (26, 3) to (0, 22)?Write your answer as a function(x, y) (?, ?).D. a reflection across the line y 5 312. How is the point (3, 25) related to its reflectionacross the line y 5 2?A. The point (3, 25) and its image are 2 units apart.B. The point (3, 25) is on the line of reflection.C. The point and its image are the same distancefrom the line y 5 2.D. The line of reflection is perpendicular to theline y 5 2. 2015 College Board. All rights reserved.3SpringBoard Geometry, Unit 2 Practice
Nameclassdate15. Construct viable arguments. Consider the capitalletters from H through P.13. The point (25, 22) is reflected over a line ofreflection. Find the equation of the line ofreflection if the image of (25, 22) is each of thefollowing.a. List the letters with no lines of symmetry.a. (5, 22)b. List the letters with exactly one line ofsymmetry.b. (25, 2)c. List the letters with exactly two lines ofsymmetry.c. (25, 0)d. Consider the four operation symbols 1, 2, 3,and 4. How many lines of symmetry does eachone have?d. (0, 22)e. (25, 22)Lesson 9-414. Model with mathematics. Use the square shown.16. Use the diagram of a T with an arrow, as shown.yy55AB525Dx525xC2525a. What are the coordinates of the image of vertex Aif the square is reflected across the line x 5 5? After each rotation of the figure, indicate thedirection of the arrow.a. 90 counterclockwiseb. What are the coordinates of the image of vertex Bif the square is reflected across the line y 5 0?b. 90 clockwisec. What are the coordinates of the image of vertex Cunder the reflection (x, y) (x, 2y)?c. 180 d. Under a reflection, vertex D maps to (0, 6).What is the line of reflection? 2015 College Board. All rights reserved.d. 270 clockwise4SpringBoard Geometry, Unit 2 Practice
Nameclassdate19. A rotation maps figure ABCDE to figure PQRST.17. Model with mathematics. Use the diagramshown. Which rotation maps Figure II ontoFigure I?a. What angle of PQRST must have the samemeasure as angle D?y5b. What angle of ABCDE must have the samemeasure as angle T?25I5xc. What side of PQRST must have the same lengthas BC ?II25d. What general property can you use to answerParts a through c?A. a rotation of 180 around (5, 25)B. a rotation of 90 clockwise around (3, 23)20. Attend to precision. Describe the rotation thatwould move the arrow from (22, 1) to eachposition.C. a rotation of 90 counterclockwise around(5, 23)D. a rotation of 90 clockwise around (5, 23)y518. In the diagram, figure IV is the rotated image offigure III.y525x5III25525xa. pointing up, with the tip at (22, 7)IV25b. pointing left, with the tip at (24, 3)a. What is the center of rotation?c. pointing right, with the tip at (5, 22)b. What are the angle and direction of rotation?d. pointing up, with the tip at (2, 1) 2015 College Board. All rights reserved.5SpringBoard Geometry, Unit 2 Practice
Nameclassdate25. Which of the following statements is NOT true?Lesson 10-1A. The composition of two translations can berepresented as a single translation.21. Write the notations for these compositions oftransformations.a. a reflection about the line x 5 2, followed by arotation of 180 about the originB. The composition of two rotations can berepresented as a single rotation.C. The composition of two reflections can berepresented as a single reflection.D. The composition of a translation followed by areflection can be represented as the compositionof a reflection followed by a translation.b. a translation of the directed line segment fromthe origin to (0, 5), followed by a reflectionaround the line y 5 5Lesson 10-226. Consider the figures in the diagram shown.Complete each transformation or composition toshow the two rectangles are congruent.A22. Reason quantitatively. An arrow is placed withits base at (21, 1) and its tip at (4, 1). Identify thepositions of the image’s base and tip underthe composition T(3, 21) ((R0, 90 ) T(2, 3)).BmGDC23. Identify the inverses of these transformations andcompositions.Fa. T(5, 21)a. reflection of ABCD over ?b. R0, 180 (T(2, 3))b. translation of DEFG by directed line segmentDC , followed by rotation ?24. Attend to precision. For each of thesecompositions, identify the single rigid motionthat performs the same mapping.c. rotation of DEFG 90 clockwise around D,followed by translation ?a. R(3, 4), 90 (R(3, 4), 90 )d. rotation of DEFG 90 clockwise around D,followed by reflection ?b. 2T(2, 23) (T(25, 5)) 2015 College Board. All rights reserved.E6SpringBoard Geometry, Unit 2 Practice
Nameclassdate30. In the diagram shown, ACFD and CHGB arerectangles, CF and CB have the same length, andAC and CH have the same length. Explain whythe following composition shows that ACFD and CHGB are congruent.27. Reason abstractly. Explain why it is possible thatthe diameter of one circle can be congruent to theradius of another circle.28. Which combination shows that rectangles A and Bare congruent?RC, 90 (TCA (CHGB))yABC5EA255BFD10xGHLesson 11-12531. Suppose you have a sequence of rigid motions tomap XYZ to PQR. Fill in the blank for eachtransformation.A. R(0, 3), 90 (T(23, 0) (A))B. T(23, 21), 90 (R(23, 2), 90 (A))a. Y ?C. T(23, 21), 90 (R(23, 2), 90 (B))D. T(23, 27), 90 (R(23, 27), 90 (A))b. ? P29. Express regularity in repeated reasoning. ArrowA is placed with its base at (1, 3) and its tip at (6, 3).For each arrow, complete the rigid motion orcomposition that shows the new arrow iscongruent to the original one.c. YZ ?d. ? PRe. ? RPQa. base (6, 23), tip (1, 23); translation ?followed by reflection ?32. ABC is divided into two congruent triangles byBP . Fill in the blanks to show the congruent sidesand angles.b. base (6, 23), tip (1, 23); rotation ?BAPCa. AP ?c. base (6, 23), tip (1, 23); reflection ? followedby another reflection ?b. APB ?c. ? PCBd. base (0, 2), tip (26, 2); rotation ? followed bytranslation ? 2015 College Board. All rights reserved.d. PBA ?7SpringBoard Geometry, Unit 2 Practice
NameclassLesson 11-233. MNT RPQ. Complete the following.a. Name three pairs of corresponding sides.36. Write the triangle congruence criterion illustratedby each pair of triangles.a.b. Name three pairs of corresponding angles.34. Critique the reasoning of others. In the figure, DGF EFG. Which statement is NOT correct?FDdateb.Ec.GA. DG EFB. FD GEd.C. DFG EGFD. DGF EGF37. Make use of structure. Which additional sides orangles must be congruent in order to use the giventriangle congruence criterion?35. Make use of structure. For each diagram, writethe congruence criterion that can be used to showthe triangles are congruent.a. ASAAa.DBECFb.b. AASEAc.AFBBCCDDDB bisects ADC and ABC.c. SSSAd.B 2015 College Board. All rights reserved.8DCFESpringBoard Geometry, Unit 2 Practice
Nameclassd. SASdateLesson 11-3ACDB41. Suppose you are given that ABC and XYZsatisfy the ASA triangle congruence criterion.How can you show that ABC is congruent to XYZ using the definition of congruence?FE42. Construct viable arguments. You are given that ABC DCB, BD bisects ABC, and CAbisects BCD.38. Which statements are NOT enough to show that AED BEC?BC12CEABEDAa. How do you know that 1 2?DA. D C, AE BE , AED BECb. What triangle seems to be congruent to ABC?B. A B, AE BE , AED BECC. AE BE , AED BEC, DE CEc. What side is common in the two triangles?D. AE BE , AED BEC, AD BCd. What triangle congruence criterion can you useto prove the two triangles are congruent?39. Construct viable arguments. Can an obtusetriangle be congruent to an isosceles triangle?Explain.43. In the diagram shown, ABD is a reflection imageof ABC over AB . Which relationship CANNOTbe established using the properties of reflection?40. Use the diagram shown. Find two possible orderedpairs for point F so that ABC EDF.Ay105(2, 5)AC210B. CAD is a right angle.B(2, 3)25DA. AC AD(24, 3)CBD(4, 21)5E(6, 21)10C. C DxD. BC BD25 2015 College Board. All rights reserved.9SpringBoard Geometry, Unit 2 Practice
Nameclass47. Reason quantitatively. In the diagram shown, A and X are right angles.44. Make use of structure. In the diagram shown, PQR and SRQ are right angles and PR SQ .PdateyQ20SR10a. What other congruence statement aboutsegments can you make about the diagram?X(24, 21)A(3, 4)C(15, 4)10220Z (216, 21)b. What triangle congruence criterion can you useto conclude that the two triangles arecongruent?B (3, 9)20xY (24, 26)210c. Complete this statement: RSQ ? .220a. Are ABC and XYZ right triangles? Explain.d. Once the triangles are shown to be congruent,what other relationships must be true aboutpairs of sides and angles?b. Use the Distance Formula to find BC and YZ.c. Use the Distance Formula to find AB and XY.45. Suppose MNP QRS. If m M 5 47 ,m N 5 52 , and m S 5 7x 1 4, find x.d. Do you have enough information to prove that XYZ ABC? Explain.Lesson 11-446. Make use of structure. In triangles PQR and STV,what information satisfies the HL congruencecriterion?P48. In the diagram shown, YW bisects XYZ and XWZ. Which triangle congruence criterion letsyou conclude that XYW ZYW?SXQRTVYA. Q and T are right angles, PQ ST, andPR SV.ZA. HLB. Q and T are right angles, PQ ST, andQR TV.B. ASAC. SASC. Q T, PQ ST, PR SVD. SSSD. Q and T are right angles, P S, and R V. 2015 College Board. All rights reserved.W10SpringBoard Geometry, Unit 2 Practice
Nameclass49. In an isosceles triangle, a segment joins the vertexof the triangle to the midpoint of the third side.date50. In this diagram, PQ PR and PS bisects QPR.Pa. How is that segment related to the vertex angleof the triangle?Qb. Describe the angle formed by that segment andthe side it intersects.SRa. Complete this statement: SQP ? .b. How is PS related to QR?Lesson 12-151. Use appropriate tools strategically. Rewrite this flowchart proof as a two-column proof.Given: 1 4, MN PTProve: MNT TPMM1N23PT41. /1 /43. /2 /3GivenTransitive prop.2. /1 /2/3 /44. MN PT6. nMNT nTPMVertical /s are .GivenSAS5. MT TMReflexive PropertyStatementsReasons1. a.1. Given2. 1 2, 3 42. b.3. c.3. Transitive Property4. d.4. Reflexive Property5. e.5. SAS 2015 College Board. All rights reserved.11SpringBoard Geometry, Unit 2 Practice
Nameclassdate52. Use appropriate tools strategically. A plan for this proof appears below the diagram.Given: m QPS 5 m TPRPR PS, QRP TSPProve: PQR PTSPQRTSFollow the plan to complete the flowchart proof.Plan: Subtract m RPS from m QPS and from m TPR to show that QPR TPS.Then use the other given angles and sides to show that PQR PTS by ASA.1. a.Angle Addition Postulate2. m/QPR 5 m/QPS 2 m/RPSm/TPS 5 m/TPR 2 m/RPSb.3. m/QPS 5 m/TPR5. d.GivenSubst. and Trans. Prop.4. m/RPS 5 m/RPS6. PR PS,/QRP /TPSc.Given7. nPQR nPTSe.53. In a flowchart proof, suppose Statement 5 is thattwo triangles are congruent by SAS. Describe thestatements that should precede Step 5.Which could be the last two statements of the proof?A. 3 4, 1 2B. PQ SR, 1 2C. SRV QPT, 3 4D. SRV QPT, 1 254. A student wrote a correct proof for this problem.55. In a flowchart proof, suppose a statement in themiddle of the proof is that two triangles arecongruent. What will be the reason for the NEXTstatement in the proof?Given: SV TQ, VR TP, 3 4Prove: 1 2PV2Q34S1T 2015 College Board. All rights reserved.R12SpringBoard Geometry, Unit 2 Practice
NameclassdateLesson 12-2Lesson 13-156. How are the Statements and Reasons in a twocolumn proof related to the boxes and the linesbelow them, in a flowchart proof?61. Use the figure to find the missing angle measures.1 140 80 57. What do the arrows in a flowchart proof represent?2358. Use appropriate tools strategically. The firststep in a flowchart proof is that AB intersects BC atpoint M, the midpoint of BC . If an arrow leads tothe next step, which of the following could be thenext step in the proof?a. m 1 1 m 2 5b. m 1 5A. BM 5 MCc. m 3 5B. BM 1 MC 5 BCd. m 2 5C. BMA CMA62. Use the figure to find each measure.D. AM 5 MBP(3x 1 4) (2x 1 1) 59. A student is writing a flowchart proof. A part of theflowchart proof is shown below.RSnPQR nWXYAASQ(6x 2 7) a. m P 5CPCTCb. m Q 5Which statement could appear in the empty box?A. P Wc. m PRQ 5d. m PRS 5B. PQ WX63. Model with mathematics. In the diagram shown,lines m and n are parallel.C. PR WYD. P and R are complementary angles.Find the measure of ABC.A60. Reason abstractly. It is given that FJ HG andFG HJ . Is 1 2? Explain your answer inparagraph form.FJmB230 Ca. Redraw the diagram in Item 63, and add a linethrough B that is parallel to m and n. Explainhow to use your diagram to find m ABC.b. Redraw the original diagram and extend CBthrough line m. Explain how to use yourdiagram to find m ABC.H 2015 College Board. All rights reserved.?nG150 13SpringBoard Geometry, Unit 2 Practice
NameclassUse 1, 2, or 3 to complete the statements.64. a. Persevere in solving problems. In thediagram, M is the midpoint of AC. ABC isrotated 180 about M.Adate DCP ? CDP ?D P ?1c. List the three angles that have their vertex atpoint C.M23BCd. How is your result in Part c related to theTriangle Sum Theorem?Use 1, 2, or 3 to complete the followingstatements: ADC ? ,65. Which statement is NOT correct? ACD ? ,A. An exterior angle of a triangle can equal one ofthe interior angles of the triangle. CAD ? .b. The diagram below extends the diagram inPart a by translating ABC along the directedsegment BC.AB. An exterior angle of a triangle can be acute,right, or obtuse.C. A triangle can have two exterior angles that areobtuse angles.D1D. A triangle can have two exterior angles that areacute angles.M23BCPLesson 13-266. Use appropriate tools strategically.Use the lines below the flowchartproof to complete the proof of theIsosceles Triangle Theorem, usingthe altitude from the vertex angle.Given: TM 5 TNMNTP1. TP ' MNGiven3. nTMP and nTNPare right triangles.2. /TPM and /TPNare right angles.a.Perpendicular lines form right angles. Prove: M N4. b.6. nTPM nTPNReflexive Propertyc.M5. TM 5 TNTGivenPN7. d.e.a.b.c.d.e. 2015 College Board. All rights reserved.14SpringBoard Geometry, Unit 2 Practice
NameclassdateLesson 14-167. Reason quantitatively. In an isosceles triangle,the bisector of the vertex angle forms an angle of27 with each leg. What are the base angles of thetriangle?71. Consider the diagram shown.y1068. a. State the Converse of the Isosceles TriangleTheorem.C (11, 5)5A (1, 1)b. Use this information to prove the Converse ofthe Isosceles Triangle Theorem. Write yourproof as a paragraph proof.XWB (7, 1)051015xa. Use the diagram to show the altitudes of ABC.Y1 2ZGiven: m X 5 m YZW bisects XZY.b. For ABC, do the altitudes intersect inside, on,or outside the triangle?Prove: XZ YZ69. One angle of an isosceles triangle is 40 . Which ofthe following CANNOT describe the triangle?A. The triangle can be obtuse.B. The triangle can be right.C. Another angle of the triangle can be 70 .c. Is your answer to Part b related to the shape of ABC? Explain.D. Another angle of the triangle can be 100 .70. In an isosceles triangle, the measure of a baseangle is (2x 1 5) . At the vertex, the measureof an exterior angle is (5x 2 3) .a. Write and solve an equation to find x. Explainwhat properties you used to write the equation.d. Find the point of intersection of the altitudes.b. Find the measures of the angles of the triangle. 2015 College Board. All rights reserved.15SpringBoard Geometry, Unit 2 Practice
Nameclass72. Attend to precision. Find an ordered pair forthe orthocenter of the triangle with verticesM(26, 22), N(2, 6), and P(4, 0).75. Express regularity in repeated reasoning. Thealgebraic process of finding the orthocenter of atriangle uses equations for the altitudes of thetriangle. If you know the coordinates of the verticesof a triangle, explain the steps you take to find theequation of any altitude.73. In the diagram of QRS and its three altitudes,m RQS 5 86 and m QSR 5 40 . Find themeasure of each angle.Lesson 14-2QVdateT76. Consider the diagram shown.Yy5P(0, 3)RQ(6, 0)WS510xR(0, 23)a. m QRT 5 ?25a. Use the diagram to show the medians of PQR.b. m VSR 5 ?c. m WQS 5 ?b. For PQR, do the medians intersect inside, on,or outside the triangle?d. m VYQ 5 ?e. m QYS 5 ?c. Is your answer to Part b related to the shape of PQR? Explain.74. Suppose RPQ is either an acute triangle oran obtuse triangle. Which of the following canbe true?A. The orthocenter can be on the triangle.d. Find the point of intersection of the medians.B. The orthocenter must be outside the triangle.C. The orthocenter must be inside the triangle.D. The orthocenter cannot be on the triangle. 2015 College Board. All rights reserved.16SpringBoard Geometry, Unit 2 Practice
NameclassLesson 14-377. Express regularity in repeated reasoning. Findthe centroid for the triangle whose vertices areF(23, 6), G(3, 6), and H(9, 26).81. Consider the diagram shown.y109876V (0, 5)54321X (7, 0)W (0, 0)x1 2 3 4 5 6 7 8 9 1078. Attend to precision. In the diagram of CDE andits medians, CJ 5 3, HJ 5 4.5, and CD 5 12. Findthe following lengths.CFHJDEdateGa. Use the diagram to show the perpendicularbisectors of the sides of VWX.a. JG 5 ?b. HD 5 ?b. For VWX, is the intersection of theperpendicular bisectors inside, on, or outsidethe triangle?c
SpringBoard Geometry, Unit 2 Practice LeSSon 10-1 21. A.Write the notations for these compositions of transformations. a.a reflection about the line x 5 2, followed by a rotation of 180 about the origin b. a translation of the directed line segment from the origin to (0, 5), followed by a reflection around the line y 5 5 22. Reason .
Geometry Unit 10: Circles Name_ Geometry Unit 10: Circles Ms. Talhami 2 Helpful Vocabulary Word Definition/Explanation Examples/Helpful Tips Geometry Unit 10: Circles Ms. Talhami 3 Equation of a Circle Determine the center an
Name Class Date Reteaching Parallel Lines and Triangles Triangle Angle-Sum Theorem: . Name Class Date In the diagram at the right, 1 is an exterior angle of the triangle. An exterior angle is an angle formed by one side of a polygon and an . Analytic Geometry Unit 1: Similarity, Congruence & Proofs Lesson 7 .
course. Instead, we will develop hyperbolic geometry in a way that emphasises the similar-ities and (more interestingly!) the many differences with Euclidean geometry (that is, the 'real-world' geometry that we are all familiar with). §1.2 Euclidean geometry Euclidean geometry is the study of geometry in the Euclidean plane R2, or more .
www.ck12.orgChapter 1. Basics of Geometry, Answer Key CHAPTER 1 Basics of Geometry, Answer Key Chapter Outline 1.1 GEOMETRY - SECOND EDITION, POINTS, LINES, AND PLANES, REVIEW AN- SWERS 1.2 GEOMETRY - SECOND EDITION, SEGMENTS AND DISTANCE, REVIEW ANSWERS 1.3 GEOMETRY - SECOND EDITION, ANGLES AND MEASUREMENT, REVIEW AN- SWERS 1.4 GEOMETRY - SECOND EDITION, MIDPOINTS AND BISECTORS, REVIEW AN-
At Your Name Name above All Names Your Name Namesake Blessed Be the Name I Will Change Your Name Hymns Something about That Name His Name Is Wonderful Precious Name He Knows My Name I Have Called You by Name Blessed Be the Name Glorify Thy Name All Hail the Power of Jesus’ Name Jesus Is the Sweetest Name I Know Take the Name of Jesus
Trigonometry Unit 4 Unit 4 WB Unit 4 Unit 4 5 Free Particle Interactions: Weight and Friction Unit 5 Unit 5 ZA-Chapter 3 pp. 39-57 pp. 103-106 WB Unit 5 Unit 5 6 Constant Force Particle: Acceleration Unit 6 Unit 6 and ZA-Chapter 3 pp. 57-72 WB Unit 6 Parts C&B 6 Constant Force Particle: Acceleration Unit 6 Unit 6 and WB Unit 6 Unit 6
Accelerated CCGPS Analytic Geometry B/Advanced Algebra - At a Glance . Common Core Georgia Performance Standards: Curriculum Map 1. st Semester nd2 Semester Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10 Extending the Number System Quadratic Functions Modeling Geometry Applications of Probability Inferences and
1-7 uij it t/j p \1 tfl)n t:"!-n!,--sl tt}j11e dat e i glli\de i urj 11 sign i\ l ull e date i gilade i unit signa t ulle date i grade l unit signa t ulle date igr de i unit sig na t ulle date igradei unit signature date r ll/\de., unit sig ijatuile date i grade i unit sig nature date rf1ade 1 un it sig nature diite rlli\d f. i unit
