The Geometry Semester A Examination will have the following types of items:

Transcription

1 The Geometry Semester Examination will have the following types of items: Selected Response Student Produced Response (Grid-Ins) Short nswer calculator and patty paper may be used. compass and straightedge will be required. Note: Figures are NOT drawn to scale. The formulas below will be provided in the examination booklet. Polygon ngle Formulas Let n be the number of sides of a polygon. Sum of the degree measures of the interior angles of a polygon = 180 o n 2 Degree measure of an interior angle of a regular polygon = o 180 n 2 n Coordinate Geometry Formulas Let, and, x y x y be two points in the coordinate plane y2 y1 The slope of is, where x1 x2. x x The midpoint of has coordinates x x, y y The distance from point to point is x x y y MCPS

2 1. Name the three undefined terms of geometry. 2. How many different lines are determined by two points? 3. How many different lines are determined by three noncollinear points? 4. How many different planes are determined by three noncollinear points or by two intersecting lines? 5. On a number line, point has a coordinate of 5, and point is on the same line with 13. What are the two possible coordinates of point? 6. On a number line, points,, and C have coordinates a, b, and c with a b c. If a 9, C 21, and 2C, what are the values of b and c? 7.,, and C are three collinear points such that 12, C 2, and C 10. Is point between points and C? Justify your answer. For items 8 through 10, points,, and C are collinear with between and C. 8. If C 20 and C 12, then. 9. If x, C 2x 30, and C 90, then x. 10. If 2x 10, C 5x 40, and C 9x 70, what is the length of C? For items 11 through 14, points,, and C are collinear, with the midpoint of C. 11. If 6, then C. 12. If 3x 20, and C 50, then x. 13. If 4x 20, and C 6x 30, then x. 14. If 5x 30, and C 12x 10, then x. 15. Points E, F, G, and H line on a line, in that order. a. If EF GH, name another pair of congruent segments. b. If EF GH, EH 50, and FG 36, what is the length of EG? MCPS

3 The figure below will be used for items 16 through If m o, what is the measure of 2? 17. If m 1 4x 20 o and m 2 x 10, what is the value of x? 18. If m 1 6x 38 o and m 2 4x 22, what is the measure of 1? o o o 19. In the figure below, D m C x m CD x, 2 20, and o C a. What is the value of x? D b. What is the measure of C? 20. Look at the figure below. The three segments intersect in one point. 4x o y o 40 o 3x o Find the values of x and y. MCPS

4 For items 21 through 25, write a rule in the form F x, y?,? that describes the given transformations. 21. x, y is reflected about the x-axis. 22. x, y is reflected about the y-axis. 23. x, y is translated five units right. 24. x, y is rotated 180 degrees about the origin. 25. x, y is translated three units down. 26. Which of the following describes transformations such as reflections, rotations, and translations, in which the preimage and image are congruent? congruent similar C rigid D regular 27. Look at the line segment on the coordinate plane below. y O x a. Reflect about the x-axis. Name the reflected segment. b. Translate five units right. Name the translated segment. c. Write the coordinates of and. d. If point P x, y is on, what are the coordinates of points P and P? MCPS

5 28. Look at this conditional: If an animal is a dog, then the animal is warm-blooded. a. Draw an Euler diagram for the conditional. b. Write the converse of the conditional. c. Write the inverse of the conditional. d. Write the contrapositive of the conditional. e. For the conditional If an animal is a dog, then the animal is warm-blooded, which statement(s) is true, the converse, inverse, or its contrapositive? 29. Look at this conditional: If a person is between the ages of 13 and 19 (including 13 and 19), then the person is a teenager. a. Write the converse of the conditional. b. Write the inverse of the conditional. c. Write the contrapositive of the conditional. d. For the conditional If a person is between the ages of 13 and 19, (including 13 and 19), then the person is a teenager, which statement(s) are true; the converse, inverse, or contrapositive? 30. Look at this conditional: If you are 20 years old, then you can vote. a. Draw an Euler diagram for this conditional. b. Use the Euler diagram to evaluate the statement: If you vote, then you are 20 years old. 31. Look at the premises below: o If Chris earns $10, then he will go to the game. o If Chris goes to the game, he will take Jane o Chris earns $10. Write all valid conclusions from the premises above. MCPS

6 For items 32 and 33, write a valid conclusion from the statements. 32. If a triangle is equilateral, then the triangle is equiangular. Triangle C is equilateral. 33. If Sally studies for a test, then she will pass the test. Sally does not pass the test. 34. Which of the following is always logically equivalent to a conditional statement? Converse Inverse C Contrapositive D None For items 35 through 38, state whether inductive or deductive reasoning is used. 35. The Cubs have not won a World Series in 109 years. They will not win a World Series this year. 36. ll squares have congruent diagonals. If I construct a square, it will have congruent diagonals. 37. If an animal is a black bear, it will hibernate in the winter. I saw a black bear. Therefore, I conclude that it will hibernate in the winter. 38. I saw a pattern of numbers 12, 11, 14, 9, 16, 7. I think the next two terms in the pattern are 18, Make a logical chain from these statements o Statement #1: If I go to the store, then I will buy candy. o Statement #2: If I buy candy, then I will not eat my dinner. o Statement #3: If it is sunny outside today, then I will go to the store. 40. Make a logical chain from these statements o Statement #1: If I get a reward, then it will be a video game. o Statement #2: If I do my homework, then I will do well on my test. o Statement #3: If I do well on my test, then I will get a reward. o Statement #4: If I listen carefully in class, then I will do my homework. MCPS

7 41. Determine the number of lines of symmetry for each figure. a. square b. regular octagon c. circle 42. Draw any lines of symmetry on the figure below. 43. Look at the regular pentagon below. Which of the following is NOT a possible measure of the pentagon s rotational symmetry? C D 36 o 72 o 144 o 216 o MCPS

8 44. Place an X in the boxes where the property is true. Property Parallelogram Rectangle Square Rhombus Trapezoid Opposite sides congruent Exactly one pair of sides parallel Opposite angles congruent Diagonal forms 2 congruent triangles Diagonals bisect each other Diagonals congruent Diagonals perpendicular Diagonal bisects opposite angles ll angles are right angles ll sides are congruent 45. In the figure below, p q r. 55 o p x o q 40 o r What is the value of x? 46. In the figure below lines p and q are parallel. p q Determine the values of x and y. MCPS

9 47. Look at the figure below. l m n 2 p For each statement given below, state which pair of lines can be proven parallel. Justify your answer. a. 1 2 b. 3 4 c. 4 and 5 are supplementary. 48. Look at isosceles triangle C below. 120 o x o What are the values of x and y? 49. Look at the triangle below. 12 b o Which of the following statements is true about a, b, and c? b a c b c a C c a b D a c b c o a o MCPS

10 For items 50 through 53, grid in and bubble in your answers on the grids below. 50. Find the sum of the interior angles of a dodecagon (12 sides). 51. Find the measure of each interior angle of a 15-sided polygon. 52. Determine the measure of each exterior angle of a regular nonagon (9-sided). 53. The measure of exterior angle of a regular polygon is 45 o. How many sides does this polygon have? / / /..... / / /..... / / /..... / / / Two sides of a triangle measure 6 and 9. Complete the statement below by putting the appropriate numbers in the blanks. The third side must be longer than and shorter than. 55. Find the value of y in the figure below. MCPS

11 For items 56 through 59, find the value of x and/or y in each figure x 5 y 11 9 x Graph the points 3,2, 1, 2, C 2, 5,and D 4, 1 on the coordinate plane. What type of quadrilateral is CD? Justify your answer using slope computations. 61. Points 3,4, 4,6, and C 7,18 are three vertices of a triangle. Use slopes to determine if the triangle is a right triangle. 62. Find the midpoint of if 2,9 and 5,17. MCPS

12 63. Look at triangles C and DEF below. E C D F In parts a through f below, information is given about the two triangles. State whether the triangles can be proven congruent by S, SSS, S, or SS. If the triangles cannot be proven congruent, state why. a. EF, C DF, F. b. F, E, C D. c. F, E, EF. d. EF, C DF, C DE. e. E, C DF, C DE. f. F, EF, C D. 64. Given: D is the perpendicular bisector of C. Prove: C C. E D C MCPS

13 65. Given: D EG, C FG. Prove: CF CGF C D E F G H 66. Quadrilateral PQRS has diagonals PR and QS that intersect at point T. For the conditions given below, state which one of the following describes quadrilateral PQRS: rectangle, rhombus, square, trapezoid, or none of these figures. a. PQ RS, PQ is not congruent to RS b. PQRS is a parallelogram, PR QS c. PQRS is a parallelogram, PR QS d. QP RS 67. Perform the following constructions. Use mathematics to justify each construction. a. the perpendicular bisector of a segment b. the bisector of an angle c. a line parallel to a given line, through a point not on the line d. a point equidistant from three noncollinear points MCPS

14 68. Point P is on the angle bisector of C. Which of the following statements is true? I Point P is equidistant from and C. II P PC C D Neither statement I nor statement II is true. Only statement I is true. Only statement II is true. oth statements I and II are true. 69. Point P is on the perpendicular bisector of. Which of the following statements is true? I P P II P 1 2 C D Neither statement I nor statement II is true. Only statement I is true. Only statement II is true. oth statements I and II are true. MCPS