Review for Geometry Midterm 2015: Chapters 15


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1 Name Period Review for Geometry Midterm 2015: Chapters 15 Short Answer 1. What is the length of AC? 2. Tell whether a triangle can have sides with lengths 1, 2, and Danny and Dana start hiking from the same base camp and head in opposite directions. Danny walks 6 miles due west, then changes direction and walks for 5 miles to point C. Dana hikes 6 miles due east, then changes direction and walks for 5 miles to point S. Use the diagram to find which hiker is farther from the base camp. 4. Given: ABC MNO Identify all pairs of congruent corresponding parts. 6. What is the slope of the line shown? 5. Apply the transformation M to the triangle with the given vertices. Identify and describe the transformation. M: (x, y) (x 6, y + 2) E(3, 0), F(1, 2), G(5, 4) 1
2 7. What is the value of x? Identify the missing justifications. m PQR = x 11, m SQR = x + 1, and m PQS = 100. m PQR + m SQR = m PQS x 11 + x + 1 = 100 2x 10 = 100 2x = 110 x = 55 a. b. Substitution Property c. Simplify d. e. Division Property of Equality 8. Is the line through points P( 8, 1) and Q( 5, 8) parallel to the line through points R(3, 0) and S(1, 4)? Explain. 9. Compare m ABC and m CBD. 10. Where is the circumcenter of any given triangle? 11. Find the coordinates of the midpoint of the segment whose endpoints are H(10, 1) and K(8, 3). 2
3 12. What is the missing reason in the twocolumn proof? Given: QS bisects TQR and SQ bisects TSR Prove: TQS RQS Statements Reasons 1. QS bisects TQR 1. Given 2. TQS RQS 2. Definition of angle bisector 3. QS QS 3. Reflexive property 4. SQ bisects TSR 4. Given 5. TSQ RSQ 5. Definition of angle bisector 6. TQS RQS 6.? 13. What is the value of x? 15. Write an equation in slopeintercept form of the line through point P(1, 4) with slope Complete the twocolumn proof. Given: x = Find the value of x for which l is parallel to m. The diagram is not to scale. Prove: x = 10 x + 9 = 11 a. 5 x 5 = 2 b. x = 10 c. 3
4 17. Find the value of x. The diagram is not to scale. 18. NPM? 19. Tom is wearing his favorite bow tie to the school dance. The bow tie is in the shape of two triangles. Given: AB ED, BC DC, AC EC, A E Prove: ABC EDC Complete the proof. Proof: Statements Reasons 1. AB ED, BC DC, AC EC 1. Given 2. A E 2. Given 3. BCA DCE 3. [1] 4. B D 4. [2] 5. [3] 5. Definition of congruent triangles 4
5 20. Given: P is the midpoint of TQ and RS. Prove: TPR QPS Complete the proof. Proof: Statements 1. P is the midpoint of TQ and RS. 1. Given Reasons 2. TP QP, RP SP 2. [1] 3. [2] 3. Vertical Angles Theorem 4. TPR QPS 4. [3] 21. Determine whether triangles EFG and PQR are congruent. 23. Find m K. 24. If EF = 8x + 13, FG = 16, and EG = 85, find the value of x. The drawing is not to scale. 22. If Z is the midpoint of RT, what are x, RZ, and RT? 5
6 25. The diagram shows the approximate distances from Houston to Dallas and from Austin to Dallas. What is the range of distances, d, from Austin to Houston? Use the diagram to find the following. 26. What are the measures of ABD and ABC? Classify each angle as acute, right, obtuse, or straight. 28. Identify a pair of alternate exterior angles. 29. Find the value of x. The diagram is not to scale. 27. Find the value of x. The diagram is not to scale. 30. What additional information do you need to prove ABC ADC by the SAS Postulate? 6
7 31. In ACE, G is the centroid and BE = 15. Find BG and GE. 36. Justify the last two steps of the proof. Given: PQ SR and PR SQ Prove: PQR SRQ 32. Write the sides of IJK in order from shortest to longest. 33. Tell whether a triangle can have sides with lengths 5, 11, and MO bisects LMN, m LMO = 8x 28, and m NMO = 2x Solve for x and find m LMN. The diagram is not to scale. Proof: 1. PQ SR 1. Given 2. PR SQ 2. Given 3. QR RQ 3.? 4. PQR SRQ 4.? 37. Supplementary angles are two angles whose measures have a sum of. Complementary angles are two angles whose measures have a sum of. 38. The legs of an isosceles triangle have lengths 3x + 2 and x The base has length 2x + 2. What is the length of the base? 39. For these triangles, select the triangle congruence statement and the postulate or theorem that supports it. 35. The lengths of two sides of a triangle are 3 inches and 8 inches. Find the range of possible lengths for the third side, s. 7
8 40. ABC is an isosceles triangle. AB is the longest side with length 10x + 3. BC = 5x + 5 and CA = 4x Find AB. 41. Name the line and plane shown in the diagram. 42. What are the names of four coplanar points? 43. Find the value of x. 8
9 44. Name the angle included by the sides MP and PN. 45. Find the value of k. The diagram is not to scale. Multiple Choice Identify the choice that best completes the statement or answers the question. 46. Write an equation in pointslope form & slope intercept form of the line through point J(10, 2) with slope 7. a. y + 2 = 7( x + 10) c. y 2 = 7( x + 10) b. y + 2 = 7( x 10) d. y + 2 = 7( x 10) 47. Which two lines are parallel? I. 5y = 4x 5 II. 7y = 5 5x III. 7y + 5x = 1 a. I and III c. II and III b. I and II d. No, two of the lines are parallel. 48. Where can the bisectors of the angles of an obtuse triangle intersect? I. inside the triangle II. on the triangle III. outside the triangle a. I only b. III only c. I or III only d. I, II, or II 9
10 49. Supply the missing reasons to complete the proof. Given: A D and AC DC Prove: BC EC Statement 1. A D and AC DC Reasons 1. Given 2. BCA ECD 2. Vertical angles are congruent. 3. BCA ECD 3.? 4. BC EC 4.? a. ASA; Corresp. parts of are. c. AAS; Corresp. parts of are. b. ASA; Substitution d. SAS; Corresp. parts of are. 50. Which statement can you conclude is true from the given information? Given: AB is the perpendicular bisector of IK. a. A is the midpoint of IK. c. AJ = BJ b. IJ = JK d. IAJ is a right angle. 10
11 Review for Geometry Midterm 2015: Chapters 15 Answer Section SHORT ANSWER No 3. Danny is farther from the base camp than Dana. 4. A M, B N, C O, AB MN, BC NO, AC MO 5. This is a translation 6 units left and 2 units up Angle Addition Postulate; Addition Property of Equality 8. No; the lines have unequal slopes. 9. m ABC > m CBD 10. the point of concurrency of the bisectors of the angles of the triangle 11. (9, 2) 12. ASA Postulate y = 3x a. Given b. Subtraction Property of Equality c. Multiplication Property of Equality BCA 19. [1] Vertical Angles Theorem [2] Third Angles Theorem [3] ABC EDC 20. [1]. Definition of midpoint [2] TPR QPS [3] SAS 1
12 21. The triangles are congruent because EFG can be mapped to PQR by a reflection: (x,y) (x, y). 22. x = 14, RZ = 88, and RT = m K = x = < d < m ABD = 16 ; ABD is acute. m ABC = 180 ; ABC is straight and ACB ACD 31. BG = 5, GE = JK, IK, IJ 33. Yes 34. x = 11, m LMN = < s < Reflexive Property of ; SSS ; ABC JKL, HL 40. AB = MN and plane M NP 42. Points D, A, B, and J are coplanar P MULTIPLE CHOICE 46. B 47. C 48. A 49. A 50. B 2
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