GH Midterm Exam Review #1 (Ch 1-4)

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1 Nme Period Due Monday, 11/ Points for completion. GH Midterm Exam Review #1 (Ch 1-4) 1. If EF=2x 12,FG=3x 15,andEG=23, find the values of x, EF, and FG. The drawing is not to scale. 7. Find the circumference of the circle to the nearest tenth. Use 3.14 for π. 2. If m DEF=122, then what are m FEG and m HEG? The diagram is not to scale. 3. MO bisects LMN, m LMO = 6x 22, and m NMO = 2x +34. Solve for x and find m LMN. The diagram is not to scale. 8. If the perimeter of a square is 72 inches, what is its area? 9. If m AOC=85, m BOC=2x+10, and m AOB=4x 15, find the degree measure of BOC and AOB. The diagram is not to scale. 10. If m EOF = 26 and m FOG = 38, then what is the measure of EOG? The diagram is not to scale. 4. T(8, 15) is the midpoint of CD. The coordinates of D are (8, 20). What are the coordinates of C? 5. Find the distance between points P(8, 2) and Q(3, 8) to the nearest tenth. 6. A high school soccer team is going to Columbus, Ohio to see a professional soccer game. A coordinate grid is superimposed on a highway map of Ohio. The high school is at point (3, 4) and the stadium in Columbus is at point (7, 1). The map shows a highway rest stop halfway between the cities. What are the coordinates of the rest stop? What is the approximate distance between the high school and the stadium? (One unit 6.4 miles.) 11. Which statement is an example of the Addition Property of Equality? a. If p = q then p s=q s. b. If p = q then p+s=q+s. c. If p = q then p s=q s. d. p = q 1

2 . 12. Transitive Property of Congruence If CD EFandEF GH,then. a. EF GH b. EF EF c. CD GH d. CD EF 13. Name the Property of Congruence that justifies this statement: If A Band B C, then A C. 14. What is the value of x? 17. Find m 1 in the figure below. PQ and RS are parallel. 15. Find the values of x and y. a. 105 b. 75 c. 115 d Given: line f is parallel to line g. Find the value of x. The diagram is not to scale. 16. Line r is parallel to line t. Find m 5. The diagram is not to scale. 19. Find the values of x and y. The diagram is not to scale. 2

3 20. Find the value of x for which p is parallel to q, if m 1=4xandm 3=112.The diagram is not to scale. 21. Find the value of x for which l is parallel to m. The diagram is not to scale. 23. Name the ray in the figure. a. BA b. AB c. BA d. AB? 24. What is the name of the ray that is opposite BA 22. Find the values of x, y, and z. The diagram is not to scale. a. BD b. BA c. CA d. DA 25. Use slopes to determine whether the lines are parallel, perpendicular, or neither. AB andcdfora(3,5),b( 2,7),C(10,5),andD(6,15) a. neither c. parallel b. perpendicular 26. AB ÄCD for A(4, 5), B( 2, 3), C(x, 2), and D(6,y). Find a set of possible values for x and y. Ï a. Ê Ë Áx,yˆ y= 1 x 4 Ô Ì,x 6 Ô 3 ÓÔ Ô Ï b. Ê Ë Áx,yˆ y= 1 x 4 Ô Ô Ì 3 ÓÔ Ô Ï c. ÔÊ Ì Ë Áx,yˆ y=3x 20,y 2 Ô ÓÔ Ô Ï d. ÔÊ Ì Ë Áx,yˆ y=3x 20,x 2 Ô ÓÔ Ô 27. Write the equation of the line with slope 2 through the point (4, 7) in point-slope form. a. y=2x 1 b. y=2x+7 c. y 4=2(x 7) d. y 7=2(x 4) 28. A right triangle is formed by the x-axis, the y-axis and the line y= 2x+3. Find the length of the hypotenuse. Round your answer to the nearest hundredth. 3

4 29. Which diagram shows plane PQR and plane QRS intersecting only in QR? a. 30. Name an angle vertical to DGE. b. a. DGI b. EGJ c. JGI d. EGH 31. Name an angle adjacent to DGE. c. d. a. FGI b. EGH c. HGJ d. JGI 4

32. The lines l and m intersect at point Q. a. The lines l and m intersect at. Postulate: If two lines intersect, then their intersection is exactly one line segment. b.

Postulate: If two lines intersect, then their intersection is exactly one point. d. The point Q, P, and R lie on planes J and K.

Given ABC PQR, m B = 3v +4, and m Q = 8v 6, find m B and m Q. a. 22 b. 11 c. 10 d. 25 37. Name the theorem or postulate that lets you immediately conclude ABD CBD. 33. 34.

b. A plane contains at least three noncollinear points. c. A line contains at least two points. d. Through any three noncollinear points, there is exactly one plane.

d. If two planes intersect, then their intersection is a line. a. AAS b. SAS c. ASA d. none of these 38.

5 32. The lines l and m intersect at point Q. a. The lines l and m intersect at. Postulate: If two lines intersect, then their intersection is exactly one line segment. b. The point Q lies on line m and line l. Postulate: If two planes intersect, then their intersection is exactly one point. c. The point Q lies on line m and line l. Postulate: If two lines intersect, then their intersection is exactly one point. d. The point Q, P, and R lie on planes J and K. Postulate: If a line intersects a plane, then they intersect at exactly 3 points. 35. Given QRS TUV, QS =3v+2, and TV = 7v 6, find the length of QS and TV. a. 2 b. 9 c. 8 d Given ABC PQR, m B = 3v +4, and m Q = 8v 6, find m B and m Q. a. 22 b. 11 c. 10 d Name the theorem or postulate that lets you immediately conclude ABD CBD In the figure, line m and lie in plane A. State the postulate that can be used to show that each statement is true. Points L, and T and line m lie in the same plane. a. If two points lie in a plane, then the entire line containing those points lies in that plane. b. A plane contains at least three noncollinear points. c. A line contains at least two points. d. Through any three noncollinear points, there is exactly one plane. Line m and intersect at T. a. Through any two points, there is exactly one line. b. A line contains at least two points. c. If two lines intersect, then their intersection is exactly one point. d. If two planes intersect, then their intersection is a line. a. AAS b. SAS c. ASA d. none of these 38. Can you use the SAS Congruence Postulate to prove that the two triangles are congruent? Explain your reasoning. 39. What else must you know to prove the triangles congruent by ASA? By SAS? a. ACD CAB; AB CD b. ACD CAB; AD BC c. ADC CAB; AD BC d. ACD CAB; AD AC 5

6 40. What is the value of x? 43. Determine whether triangles EFG and PQR are congruent. a. 71 b. 142 c. 152 d The legs of an isosceles triangle have lengths 2x +4 and x +8. The base has length 5x 2. What is the length of the base? a. 18 b. 4 c. 12 d. cannot be determined 42. Find the value of x. The diagram is not to scale. a. x=23 b. x=40 c. x=13 d. none of these a. The triangles are congruent because EFG can be mapped to PQR by a reflection: (x,y) ( x,y). b. The triangles are congruent because EFG can be mapped to PQR by a rotation: (x,y) ( y, x). c. The triangles are congruent because EFG can be mapped to PQR by a reflection: (x,y) (x, y). d. The triangles are congruent because EFG can be mapped to PQR by a rotation: (x,y) ( y,x). 6

7 44. Prove that the triangles with the given vertices are congruent. A(3, 1), B(4, 5), C(2, 3) D( 1, 3), E( 5, 4), F( 3, 2) 45. Find m E and m N, given m F=m P, m E=(x 2 ), and m N=(4x 2 75). a. The triangles are congruent because ABC can be mapped onto DEF by a rotation: (x,y) (y, x), followed by a reflection: (x,y) (x, y). b. The triangles are congruent because ABC can be mapped onto DEF by a reflection: (x,y) ( x,y), followed by a rotation: (x,y) (y, x). c. The triangles are congruent because ABC can be mapped onto DEF by a translation: (x,y) (x 4,y), followed by another translation: (x,y) (x,y 6). a. m E=25, m N=25 b. m E=25, m N=65 c. m E=65, m N=25 d. m E=65, m N=65 d. The triangles are congruent because ABC can be mapped onto DEF by a rotation: (x,y) ( y,x), followed by a reflection: (x,y) (x, y). 7

8 46. Given: RT SU, SRT URT, RS RU. T is the midpoint of SU. Prove: RTS RTU Complete the proof. Proof: Statements Reasons 1. RT SU 1. Given 2. RTS and RTU are right angles. 2. [1] 3. RTS RTU 3. Right Angle Congruence Theorem 4. SRT URT 4. Given 5. S U 5. [2] 6. RS RU 6. Given 7. T is the midpoint of SU. 7. Given 8. ST UT 8. Definition of midpoint 9. RT RT 9. [3] 10. RTS RTU 10. Definition of congruent triangles a. [1] Definition of right angles [3] Transitive Property of Congruence b. [1] Definition of perpendicular lines [3] Reflexive Property of Congruence c. [1] Definition of perpendicular lines [2] Vertical Angles Theorem [3] Symmetric Property of Congruence d. [1] Definition of perpendicular lines [3] Symmetric Property of Congruence 8

9 47. 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 a. [1] Reflexive Angles Theorem [3] ABC EDC b. [1] Third Angles Theorem [2] Vertical Angles Theorem [3] ABC EDC c. [1] Vertical Angles Theorem [3] ABC EDC d. [1] Vertical Angles Theorem [3] ABC EDC 9

10 GH Midterm Exam Review #1 (Ch 1-4) Answer Section 1. x = 10, EF = 8, FG = m FEG=58, m HEG= x = 14, m LMN= (8, 10) Ê 6. 5, 5 ˆ 32 miles Ë Á 2, m in m BOC=40 ; m AOB= B 12. C 13. Transitive Property x = 15, y = A x = 77, y = x = 86, y = 75, z = A 24. A 25. A 26. A 27. D C 30. C 31. B 32. C 33. A 34. C 35. C 36. C 37. A 38. No. In order to use the SAS Congruence Postulate, the sides that form the congruent angles must be congruent. In the diagram, the right angles are congruent, but only 1 pair of sides that forms the right angle are congruent. 39. B 1

11 40. A 41. A 42. A 43. C 44. D 45. A 46. B 47. D 2

Geometry Midterm REVIEW

Geometry Midterm REVIEW Class: Date: Geometry - 2013 Midterm REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question. This diagram of airport runway intersections shows two parallel