# Geometry Midterm REVIEW

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1 Name: Class: Date: ID: A Geometry Midterm REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Given LM = MP and L, M, and P are not collinear. Draw a picture. A B C D 2. Given the conditional statement If it is July, then it is summer in the United States, write its inverse and give its truth value? F G H J 5. Which line is perpendicular to y = ? A y= B y= C y = + 10 D y = Are the graphs of the following equations coinciding, intersecting, or parallel? y= and -3y + 9 =-15 F G H J What kind of angles are <2 and <7? Identify the 2 pairs of same-side interior angles. A B C D <6= 72 and <3= 106 Can you prove that r Ä s? F G H J 7. Two congruent triangles have the following corresponding parts: RS UV, RT UW, and R U. Is triangle TRS = triangle VWU? A B C D 8. Is point (-2, 1) on the perpendicular bisector of the segment with endpoints Ê 2,5 ˆ and Ê 2, 3 ˆ? Eplain. F G H J 9. The lengths of two sides of a triangle are 4 and 9. What is the possible range of the legth measure of the third side? A B C D 1

2 Name: ID: A 10. What is the measure of <K? Classify the triangle according to its angles. 11. If y= 32, what are the values of Z and X? F G H J A B C D Short Answer 1. What is m PMN? 5. M is the midpoint of RS. R has the coordinates Ê Ë Á 6, 1 ˆ, and M has coordinates Ê 1,1 ˆ. What are the coordinates of S? 6. What is the distance from MÊ 1, 8 ˆ to NÊ 10, 4 ˆ? 2. Which angles are adjacent and form a linear pair? 7. Given a point in the coordinate plane, the rule Ê Ë Á, y ˆ Ê 1, y + 4 ˆ translates the point in which direction? 8. What is the net item in the pattern? 2, 4, 16, What is the perimeter of a square whose side is 3.6 inches? 4. Given GH with endpoints GÊ 9, 5 ˆ and HÊ 11, 3 ˆ, what are the coordinates of the midpoint of GH? 9. Write the contrapositive and give its truth value for the conditional statement If it is the weekend, then it is Saturday 10. Identify the property that justifies the statement If B = A and <A = <C, then B = C. 2

3 Name: ID: A 11. Given: 2 3, and 1 and 2 are adjacent angles whose noncommon sides form a straight line. Prove: 1 and 3 are supplementary. Complete the Two-Column Proof: 12. Write the conditional statement and converse within the biconditional. Mary can paint the entire living room if and only if she has enough paint. 13. Solve the equation 3 (2 + 1) = 27. Write a justification for each step. 3 (2 + 1) =27 Given equation =27 [1] 6 =24 [2] =4 [3] 14. Identify the property that justifies the statement. If AB CD, then CD AB 3

4 Name: ID: A 15. Use the given flowchart proof to write a two-column proof of the statement AF FD. Flowchart proof: AB = CD; BF = FC Given AB + BF = FC + CD Addition Property of Equality Complete the proof. AB + BF = AF FC + CD = FD Segment Addition Postulate AF = FD Substitution AF FD Definition of congruent segments Two-column proof: Statements Reasons 1. AB = CD; BF = FC 1. Given 2. [1] 2. Addition Property of Equality 3. [2] 3. Segment Addition Postulate 4. AF = FD 4. Substitution 5. AF FD 5. Definition of congruent segments 16. Classify BF and BC. 17. Which correctly completes the sentence? If two parallel lines are cut by a transversal, then the two pairs of corresponding angles are. 18. Given: AB EF Ä CD. E is on AB, and F is on CD. is the perpendicular bisector of CD. What is the shortest segment from E to CD? 19. Which describes the slope of a vertical line? 20. What is the slope of the line through Ê 12, 8 ˆ and Ê 6, 2 ˆ? 21. Given points AÊ Ë Á 2, 1 ˆ, B Ê Ë Á7, 2 ˆ, C Ê 2, 3 ˆ, and DÊ 3, 6 ˆ, what type of lines are AB and CD? 4

5 Name: ID: A 22. Describe the transformation M: Ê Ë Á, y ˆ Ê y, ˆ. 30. Given: GJ bisects FGH, FG HG 23. Classify the triangle. Prove: FJ HJ Proof: 24. Triangle ABC is equiangular. AB= 6 +2 and BC= What is the length of side BC? 25. What is the m U? 26. KLM RST. m L = ( 8 + 9) and m S = ( ). What is the value of? Which reason belongs in Step 6? 31. Point Z is the circumcenter of TUV. What is the value of UV? 27. What postulate or theorem justifies the congruence statement ABE CDE? 28. If A and C are right angles and AD BC, what postulate or theorem justifies the congruence statement BCD DAB? 29. Triangle ABC is equilateral. <C= 3-6. What is the value of? 5

6 Name: ID: A 32. If WX = 7.2, WL = 12.2, and KW = 16, what is the value of ZW? 38. What is another name for line n? What is another name for plane P? 33. SQ is a midsegment of NOP. What is the length of OP if SQ= 3-1 and OP= 10-14? 39. S is in between segment RT. RS= 20, ST= 3 + 4, and RT= 9. What is the measure of RT? 34. Triangle ABC is a right triangle with hypotenuse 12 and one of the legs 4. What is the lenght of the other leg in simplest radical form? 35. Which side length will form an obtuse triangle with sides of length 8 and 10? 36. Triangle ABC is a triangle with hypotenuse 7. What is the length of each leg in simplest radical form? 37. Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints A( 2,2) and B(5,4). 6

7 Geometry Midterm REVIEW Answer Section MULTIPLE CHOICE 1. ANS: D PTS: 1 DIF: Average TOP: Chapter 1 Multiple Choice Test, Form B 2. ANS: H PTS: 1 DIF: Average TOP: Chapter 2 Multiple Choice Test, Form B 3. ANS: B PTS: 1 DIF: Average TOP: Chapter 3 Multiple Choice Test, Form B DOK: DOK 1 4. ANS: H PTS: 1 DIF: Average TOP: Chapter 3 Multiple Choice Test, Form B 5. ANS: A PTS: 1 DIF: Average TOP: Chapter 3 Multiple Choice Test, Form B 6. ANS: J PTS: 1 DIF: Average TOP: Chapter 3 Multiple Choice Test, Form B 7. ANS: C PTS: 1 DIF: Average NAT: NT.CCSS.MTH G.SRT.5 TOP: Chapter 4 Multiple Choice Test, Form B 8. ANS: H PTS: 1 DIF: Average TOP: Chapter 5 Multiple Choice Test, Form B 9. ANS: D PTS: 1 DIF: Average TOP: Chapter 5 Multiple Choice Test, Form B 10. ANS: J PTS: 1 DIF: Average TOP: Chapter 5 Multiple Choice Test, Form B 11. ANS: B PTS: 1 DIF: Average TOP: Chapter 5 Multiple Choice Test, Form B SHORT ANSWER 1. ANS: ANS: 1 and 5 3. ANS: 32.8 cm 1

8 4. ANS: Ê 6, 2.5 ˆ 5. ANS: Ê 14, 8 ˆ 6. ANS: 13 units 7. ANS: 2 units to the right and 3 units down 8. ANS: 16 PTS: 1 DIF: Average TOP: Chapter 2 Multiple Choice Test, Form B 9. ANS: If a number is not divisible by 6, then it is not divisible by 3. PTS: 1 DIF: Average TOP: Chapter 2 Multiple Choice Test, Form B 10. ANS: Sym. Prop. of PTS: 1 DIF: Average TOP: Chapter 2 Multiple Choice Test, Form B 11. ANS: PTS: 1 DIF: Average TOP: Chapter 2 Multiple Choice Test, Form B 2

9 12. ANS: Conditional: If all four sides of the rectangle have equal lengths, then it is a square. Converse: If a rectangle is a square, then its four sides have equal lengths. Let p and q represent the following. p: A rectangle is a square. q: All four sides of the rectangle have equal lengths. The two parts of the biconditional p q are p q and q p. Conditional: If all four sides of the rectangle have equal lengths, then it is a square. Converse: If a rectangle is a square, then its four sides have equal lengths. PTS: 1 DIF: Average REF: 19d5c df-9c7d f0d2ea OBJ: Identifying the Conditionals Within a Biconditional Statement TOP: 2-4 Biconditional Statements and Definitions KEY: biconditional 13. ANS: [1] Addition Property of Equality; [2] Division Property of Equality 4 6 = 34 Given equation [1] Addition Property of Equality 4 = 40 Simplify. 4 = [2] Division Property of Equality = 10 Simplify. PTS: 1 DIF: Basic REF: 19dce df-9c7d f0d2ea OBJ: Solving an Equation in Algebra NAT: NT.CCSS.MTH A.REI.1 TOP: 2-5 Algebraic Proof KEY: algebraic proof proof 14. ANS: Transitive Property of Congruence The Transitive Property of Congruence states that if figure A figure B and figure B figure C, then figure A figure C. PTS: 1 DIF: Basic REF: 19e1ad3e df-9c7d f0d2ea OBJ: Identifying Properties of Equality and Congruence TOP: 2-5 Algebraic Proof KEY: congruence properties refleive symmetric transitive DOK: DOK 1 3

10 15. ANS: [1] AB + BF = FC + CD [2] AB + BF = AF ;FC + CD = FD In a flowchart, reasons flow from the statement above. The statement above Reason 2 is AB + BF = FC + CD. The statement above Reason 3 is AB + BF = AF ; FC + CD = FD. PTS: 1 DIF: Average REF: 19eb0f9e df-9c7d f0d2ea OBJ: Reading a Flowchart Proof TOP: 2-7 Flowchart and Paragraph Proofs KEY: flowchart proof two-column proof 16. ANS: perpendicular segments PTS: 1 DIF: Average NAT: NT.CCSS.MTH G.CO.1 TOP: Chapter 3 Multiple Choice Test, Form B DOK: DOK ANS: supplementary PTS: 1 DIF: Average TOP: Chapter 3 Multiple Choice Test, Form B DOK: DOK ANS: EF PTS: 1 DIF: Average TOP: Chapter 3 Multiple Choice Test, Form B 19. ANS: zero PTS: 1 DIF: Average TOP: Chapter 3 Multiple Choice Test, Form B DOK: DOK ANS: 1 3 PTS: 1 DIF: Average TOP: Chapter 3 Multiple Choice Test, Form B 21. ANS: parallel PTS: 1 DIF: Average TOP: Chapter 3 Multiple Choice Test, Form B 22. ANS: A rotation 180 with center of rotation Ê 0, 0 ˆ. PTS: 1 DIF: Average NAT: NT.CCSS.MTH G.CO.6 TOP: Chapter 4 Multiple Choice Test, Form B 4

11 23. ANS: scalene acute PTS: 1 DIF: Average TOP: Chapter 4 Multiple Choice Test, Form B DOK: DOK ANS: 8 PTS: 1 DIF: Average NAT: NT.CCSS.MTH G.SRT.5 TOP: Chapter 4 Multiple Choice Test, Form B 25. ANS: 120 PTS: 1 DIF: Average TOP: Chapter 4 Multiple Choice Test, Form B 26. ANS: 4 PTS: 1 DIF: Average NAT: NT.CCSS.MTH G.SRT.5 TOP: Chapter 4 Multiple Choice Test, Form B 27. ANS: SAS PTS: 1 DIF: Average NAT: NT.CCSS.MTH G.CO.10 NT.CCSS.MTH G.SRT.5 TOP: Chapter 4 Multiple Choice Test, Form B 28. ANS: HL PTS: 1 DIF: Average NAT: NT.CCSS.MTH G.CO.10 NT.CCSS.MTH G.SRT.5 TOP: Chapter 4 Multiple Choice Test, Form B 29. ANS: 12 PTS: 1 DIF: Average NAT: NT.CCSS.MTH G.SRT.5 TOP: Chapter 4 Multiple Choice Test, Form B 30. ANS: CPCTC PTS: 1 DIF: Average NAT: NT.CCSS.MTH G.CO.10 NT.CCSS.MTH G.SRT.5 TOP: Chapter 4 Multiple Choice Test, Form B 31. ANS: 45 PTS: 1 DIF: Average TOP: Chapter 5 Multiple Choice Test, Form B 5

12 32. ANS: 3.05 PTS: 1 DIF: Average TOP: Chapter 5 Multiple Choice Test, Form B 33. ANS: 46 PTS: 1 DIF: Average TOP: Chapter 5 Multiple Choice Test, Form B 34. ANS: 6 2 PTS: 1 DIF: Average TOP: Chapter 5 Multiple Choice Test, Form B 35. ANS: 13 PTS: 1 DIF: Average TOP: Chapter 5 Multiple Choice Test, Form B 36. ANS: PTS: 1 DIF: Average TOP: Chapter 5 Multiple Choice Test, Form B 6

13 37. ANS: y 3 = 7 ( 1.5) 2 Step 1 Plot AB. The perpendicular bisector of AB is perpendicular to AB at its midpoint. Step 2 Find the midpoint of AB. Ê Midpoint of AB = 2 + 5, ˆ 2 2 = (1.5,3) Step 3 Find the slope of the perpendicular bisector. (4) (2) Slope of AB = (5) ( 2) = 2 7 Since the slopes of perpendicular lines are opposite reciprocals, the slope of the perpendicular bisector is 7 2. Step 4 Use point-slope form to write the equation. y y 1 = m( 1 ) y 3 = 7 ( 1.5) 2 PTS: 1 DIF: Average REF: 1ad27b8a df-9c7d f0d2ea OBJ: Writing Equations of Bisectors in the Coordinate Plane NAT: NT.CCSS.MTH G.GPE.5 TOP: 5-1 Perpendicular and Angle Bisectors KEY: point-slope form perpendicular bisector coordinate geometry 38. ANS: plane BAD DOK: DOK 1 7

14 39. ANS: 40 8

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