Geometry Honors. District Midterm
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1 Geometry Honors District Midterm
2 Geometry EOC Appendix G Algebra 1 End-of-Course and Geometry End-of-Course Assessments Reference Sheet b base A area h height B area of base w width C circumference d diameter V volume r radius P perimeter slant height of base a apothem S.A. surface area V bwh V Bh or S. A. SA.. 2 bh 2 bw 2 hw or Ph 2 B V r 2 h or SA.. SA.. 2 rh 2 r 2 rh 2B 2 or V r 2 h or 1 SA.. ( 2 r ) B 2 Sum of the measures of the interior angles of a polygon Measure of an interior angle of a regular polygon where: n represents the number of sides 180 ( n 2) 180 ( n 2) n Geometry EOC Test Item Specifications Florida Department of Education G-4 137
3 Geometry EOC Appendix G Algebra 1 End-of-Course and Geometry End-of-Course Assessments Reference Sheet Slope formula Distance between two points y 2 y 1 x 2 y 2 x 2 x 1 x 1 y 1 (x 2 x 1 ) 2 + (y 2 y 1 ) 2 Midpoint between two points Slope-intercept form of a linear equation ( ( Point-slope form of a linear equation Quadratic formula - y 1 x 1 x1 y1 x Special Right Triangles x x x x x Trigonometric Ratios A sin A cos A tan A opposite hypotenuse adjacent hypotenuse opposite adjacent G-5 Geometry EOC Test Item Specifications Florida Department of Education
4 Geometry Honors District Midterm Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which one of the following is NOT one of the undefined terms in geometry? a. point c. plane b. line d. space 2. What is a valid explanation of how to construct JK so that JK! FG? a. (1) Draw a ray with endpoint J. (2) Open your compass to the length of FG. Put the compass point on G and draw an arc that intersects the ray. Label JK. JK! FG b. (1) Draw a ray with endpoint J. (2) Open your compass to the length of FG. Put the compass point on J and draw an arc that intersects the ray. Label the point of intersection K. JK! FG c. (1) Measure the segment FG. (2) Open your compass to the length of FG. Put the compass point on K and draw an arc that intersects the ray. Label the point of intersection J. JK! FG d. (1) Draw a ray with endpoint J. (2) Open your compass to the length of FG. Put the compass point on J and draw an arc that intersects the ray and is two times the length of FG. Label the point of intersection K. JK! FG 1
5 3. R is the midpoint of PS. The coordinates of S and R are given below. What are the coordinates of P? R: (5, 4) S: (6, 1) a. (4, 7) b. (10, 8) c. (5.5, 2.5) d. (7, "2) 4. An angle has a measure of What is the measure of the supplement of its complement? a c. 90 b d The circle shown below is centered at the origin and contains the point (-4, -2). Which of the following is closest to the length of the circumference of the circle? a c b d
6 6. The volume of a regular hexahedron is 216 units cubed. What is it s surface area? a. 36 units squared c. 108 units squared b units squared d. 216 units squared 7. If KM = MZ, then K is the midpoint of KZ. a. True b. False 8. Draw a Venn diagram to illustrate this conditional statement: If it is a car, then it is a motor vehicle. a. c. b. d. 3
7 9. The converse of the inverse of a conditional statement has the same truth value as which of the following? I. The original conditional statement II. The converse of the original conditional statement III. The inverse of the original conditional statement IV. The contrapositive of the original conditional statement a. I c. I and IV b. III d. II and III 10. Tien makes the following argument and reaches the conclusion below. Given: If a number is divisible by 4, then the number is divisible by is divisible by 4. Conclusion: 16 is divisible by 2. Which law guarantees Tien that she has drawn a valid conclusion? a. Law of Syllogism b. Law of Detachment c. Law of Inductive Reasoning d. Law of Conclusions 11. What is the value of c such that the points Ê Ë Á"3, 5ˆ and Ê Ë Á8, cˆ lie on a line with slope " 1 5? a. b c. 3 d If AB # CD and XY # CD, then AB is parallel to XY. a. always b. sometimes c. never 4
8 13. Complete the following truth table and choose the one that is filled out correctly below. p q r $ q r % $ q T T T T T F T T F F F F F F a. b. p q r $ q r % $ q T T T F F T T F F F T F T T T T F F T F F T T F F F T F F T F F T T F F F F T F p q r $ q r % $ q T T T F F T T F F F T F T T T T F F T F F T T F F F T F F F F F T T T F F F T F c. d. p q r $ q r % $ q T T T F F T T F F F T T T F F T T F T F F F T T T F F F T F F F T T T F F F T F p q r $ q r % $ q T T T F F T T F F F T F T T T T F F T F F T T F F F T F F F F F T T F F F F T F 5
9 14. Sebastian was asked to write the equation of the line that contains the point Ê Ë Á"1, 2ˆ and is parallel to the line y"2=3( x"1). Which equation below represents the line Sebastian is looking for in slope intercept form? a. y = 3x + 2 c. y = 3x + 5 b. y = 1 3 x + 2 d. y = " 1 3 x Complete the two-column proof. Given: 11x " 6y = "1; x = 8 Prove: 89 6 = y 11x " 6y = "1; x = 8 a. 88 " 6y = "1 b. "6y = "89 c. y = d. = y e. a. a. Given b. Symmetric Property of Equality c. Subtraction Property of Equality d. Division Property of Equality e. Reflexive Property of Equality b. a. Given b. Substitution Property c. Subtraction Property of Equality d. Division Property of Equality e. Symmetric Property of Equality c. a. Given b. Substitution Property c. Subtraction Property of Equality d. Division Property of Equality e. Reflexive Property of Equality d. a. Given b. Substitution Property c. Subtraction Property of Equality d. Division Property of Equality e. Commutative Property 6
10 16. Identify the missing justifications used to find the value of x. m&pqr = x + 7, m&sqr = x + 3, and m&pqs = 100. m&pqr + m&sqr = m&pqs x x + 3 = 100 2x + 10 = 100 2x = 90 x = 45 a. b. Substitution Property c. Simplify d. e. Division Property of Equality a. Angle Addition Postulate; Division Property of Equality b. Angle Addition Postulate; Subtraction Property of Equality c. Protractor Postulate; Addition Property of Equality d. Protractor Postulate; Subtraction Property of Equality 17. Use the diagram below, where a b. Which pair are alternate exterior angles? a. &3 and &4 c. &1 and &6 b. &1 and &2 d. &2 and &6 7
11 18. What is m&ust? a. 36 c. 104 b. 76 d Michael is building a chair for his front porch. He cuts each leg so that they form a 52 angle with the base of the seat of the chair as shown in the diagram below. What angle does the front of each leg make with the ground, x, in order to ensure that the seat of the chair is parallel with the ground? a. 138 c. 52 b. 128 d If DNP! HKF, which of the following is NOT necessarily true? a. NP! KF c. &D! &H b. DP! HF d. &P! &K 8
12 21. Which of the following is the construction of the segment that is perpendicular to AB through point C? a. c. b. d. 22. Using the information below, what is the most accurate classification of 'PQR? How long is QR? a. equilateral, QR = 24 c. acute, QR = 5.5 b. isosceles, QR = 18.5 d. equilateral, QR = 35 9
13 23. 'MNP is an isosceles triangle with MN! PN. The measure of &N is 3 times the measure of &P. What is the measure of &N? a. 144 c. 36 b. 108 d In the quadrilateral below, what is the sum of the degree measures of angles 1, 2, and 3? a. 70 c. 290 b. 110 d Find the values of x and y. a. x = 90, y = 47 c. x = 47, y = 43 b. x = 43, y = 47 d. x = 90, y = 43 10
14 26. Given: PQRS is a rectangle. Prove: PSR! QRS Which triangle congruence property is missing in step 5? Statement Reason 1. PS! QR 1. Opposite sides of a rectangle are congruent. 2. &PSR and &QRS are right angles. 2. All angles of a rectangle are right angles. 3. SR! RS 3. Reflexive Property of Congruence 4. &PSR! &QRS 4. All right angles are congruent. 5. PSR! QRS 5.? a. AAS c. SSS b. ASA d. SAS 27. To prove that parallelogram ABCD with vertices A( 5, 1), B( 9, 6), C( 1, 5), and D(3, 2) is a rhombus, you must show that it is a parallelogram with perpendicular diagonals. What are the slopes of the diagonals? a. 3 2 and " 2 3 c. 1 2 and "2 b. 1 and "1 d. " 4 7 and
15 28. What is the translation image of the triangle shown after a translation with the rule (x, y) ( (x " 3, y + 3)? a. c. b. d. 12
16 29. If a triangle is partially formed by the vertices Ê Ë "2a, 0 Ê ËÁ 2a, 0 ˆ, what is the number of unique vertices for which the triangle formed is regular? a. infinite c. 1 b. 2 d An altitude of an equilateral triangle intersects the opposite side at the midpoint. Which of the following could be used to construct an altitude of an equilateral triangle? a. copying an angle c. parallel line b. copying a segment d. perpendicular bisector 31. Where is the circumcenter of any given triangle? a. the point of concurrency of the altitudes of the triangle b. the point of concurrency of the perpendicular bisectors of the sides of the triangle c. the point of concurrency of the bisectors of the angles of the triangle d. the point of concurrency of the medians of the triangle 32. In 'ACE, G is the centroid and BE = 9. Find BG and GE. a. BG = 2 1 4, GE = c. BG = 6, GE = 3 b. BG = 3, GE = 6 d. BG = 4 1 2, GE =
17 33. Which inequality shows the possible lengths for the third side of the triangle below? a. x > 9.8 c. 3.2 < x < 6.6 b. x < 3.4 d. 3.4 < x < What is the correct order of the sides of the triangle from longest to shortest? a. LN, LM, MN c. LN, MN, LM b. LM, MN, LN d. MN, LN, ML 35. For an indirect proof of the statement below, what do you temporarily assume as the first step of the proof? The two lines are parallel. a. The two lines are NOT parallel. b. The two lines are NOT rays or segments. c. The two lines are the same. d. The two lines are skew. 36. The measure of an exterior angle of a regular polygon is 45. What type of polygon is it? a. dodecagon c. nonagon b. decagon d. octagon 14
18 37. Compare PR and QS. a. PR = QS c. PR > QS b. PR < QR d. PR < QS 38. What is the value of x in parallelogram WXYZ? a. 22 c. 12 b. 18 d LM is the midsegment of trapezoid ABCD. AB = 46 and DC = 125. What is LM? a. 171 c. 57 b d
19 40. For his mathematics assignment, Armando must determine the conditions that will make quadrilateral ABCD, shown below, a parallelogram. Given that the m&dab = 40 0, which of the following statements will guarantee that ABCD is a parallelogram? a. m&dcb = 40 0 ; m&abc = b. m&adc + m&dcb + m&abc = c. m&abc = d. m&dcb = 40 0 Short Answer 41. What is the length of RT? 42. How many edges does a triangular prism have? 43. In a regular polygon, the sum of the interior angles is equal to twice the sum of the exterior angles. What is the measure of an interior angle of the polygon? 16
20 44. To the nearest tenth, what is the length, in units, of MN? 45. Assume all angles are right angles. What is the area of the figure? 46. What is the surface area of the shoebox with the dimensions shown below? 47. An aquarium has a giant fish tank in the shape of a cylinder. To the nearest cubic foot, what is the volume of the fish tank? Use 3.14 for ). 17
21 48. In this drawing, line p is parallel to line j and line t is perpendicular to AB ** (. What is the measure of &BAC? 49. Find the x-coordinate of the circumcenter of 'ABC with vertices A("2, 4), B("2, "2), and C(4, "2). 50. Find the value of x. 18
22 Geometry Honors Mid-Term Fill-In Response Answer Sheet Name: Date: Period:
23 ID: A Geometry Honors District Midterm Exam Answer Section MULTIPLE CHOICE 1. ANS: D STA: MA.912.G ANS: B STA: MA.912.G ANS: A STA: MA.912.G ANS: D STA: MA.912.G ANS: C STA: MA.912.G ANS: D STA: MA.912.G ANS: B STA: MA.912.G ANS: A STA: MA.912.G ANS: C STA: MA.912.G ANS: B STA: MA.912.D ANS: A STA: MA.912.A ANS: B STA: MA.912.D ANS: B STA: MA.912.D ANS: C STA: MA.912.A ANS: B STA: MA.912.D.6.4 MA.912.G ANS: B STA: MA.912.D.6.4 MA.912.G ANS: D STA: MA.912.G ANS: C STA: MA.912.G ANS: B STA: MA.912.G ANS: D STA: MA.912.G ANS: D STA: MA.912.G ANS: A STA: MA.912.G ANS: B STA: MA.912.G ANS: C STA: MA.912.G ANS: D STA: MA.912.G ANS: D STA: MA.912.D.6.4 MA.912.G.4.6 MA.912.G ANS: A STA: MA.912.G ANS: C STA: MA.912.G ANS: B STA: MA.912.G ANS: D STA: MA.912.G ANS: B STA: MA.912.G ANS: B STA: MA.912.G ANS: D STA: MA.912.G ANS: C STA: MA.912.G ANS: A STA: MA.912.D ANS: D STA: MA.912.G ANS: C STA: MA.912.G ANS: B STA: MA.912.G ANS: B STA: MA.912.G.3.1 MA.912.G.3.2 MA.912.G.3.4 1
24 ID: A 40. ANS: A STA: MA.912.G.8.4 SHORT ANSWER 41. ANS: 40 STA: MA.912.G ANS: 9 STA: MA.912.G ANS: 120 STA: MA.912.G ANS: 6.7 STA: MA.912.G ANS: 360 square meters STA: MA.912.G ANS: 256 square inches STA: MA.912.G ANS: 196 ft 3 STA: MA.912.G ANS: 37 STA: MA.912.G ANS: 1 STA: MA.912.G ANS: 63 STA: MA.912.G.2.2 2
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