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HONORS GEOMETRY A Semester Exam Review
The Geometry and Honors Geometry Semester A examination will have the following types of questions:
Selected Response Student Produced Response (Grid-in) Short Answer
A calculator, scrap paper, and patty paper may be used. A compass and straightedge is required.
The formulas below will be provided in the examination booklet.
2. Complete the following with always, sometimes, or never.
a. Two points are ___________________ collinear.b. Two points are ___________________ coplanar.c. Three points are __________________ collinear.d. Three points are __________________ coplanar.
3. How many different lines are determined by two points?
4. How many different lines are determined by three noncollinear points?
5. How many different planes are determined by three noncollinear points?
6. How many planes are determined by two intersecting lines?
7. Which of the following statements are true about figures in space?
a. A line and a plane could have no points in common.b. A line and a plane could have one point in common.c. A line and a plane could have an infinite number of points in common.d. Two distinct planes could have no points in common.e. Two planes could have a line in common.
8. On a number line, point A has coordinate 5, and point D is on the line such that AD = 8. What are the two possible coordinates of point D?
9. Let A. B, and C be points on a number line with respective coordinates a, b, and c such that . If , then what are the coordinates of a and c?
For items 10 through 12, points A, B, and C are on a number line, with B between A and C.
10. If AC = 20 and BC = 12, then AB = _____
11. If AB = x, BC = , and AC = 90, then x = ______
12. If AB = , BC = , and AC = , what is the length of ? ____
29. Which of the following terms describes transformations, such as reflections, rotations, and translations, in which the preimage and image are congruent?
A Congruent
B Similar
C Rigid
D Regular
30. Look at the parallelogram on the coordinate plane below.
a. Reflect ABCD across the y-axis. Name the reflected figure .
b. Translate four units downward. Name the translated figure .
c. Write the coordinates of
d. If what are the coordinates of the transformed point on ? Explain how you determined your answer. Use words, symbols, or
44. Complete the following using indirect reasoning.
If I earn $20 this week, then I will go to a movie. I did not go to a movie. therefore, ___________________________________
For items 45 through 49, state whether inductive reasoning or deductive reasoning is used.
45. If Mr. Johns was absent on Monday, Tuesday, and Wednesday, I conclude that he will be absent on Thursday.
46. The Cubs have not won a World Series in 104 years. Therefore, they will not win this year.
47. All squares have congruent diagonals. If I construct a square, the diagonals will be congruent.
48. If an animal is a black bear, it will hibernate in the winter. I spotted a black bear; I concluded that the black bear will hibernate this winter.
49. I saw a pattern as follows: 18, 11, 20, 9, 22, 7. I concluded that the next two terms are 24,5.
50. Make a logical chain from these statements.If I go to the store, I will buy candy.If I buy candy, I will not eat my dinner.If it is sunny outside today, I will go to the store.
51. Make a logical chain from the following statements.If I get a reward, then I will buy new car.If I do well on the next test, then I will get a reward.If I buy a new car, then it will have four-wheel drive.If I do my homework, then I will do well on the next test.
52. Determine the number of lines of symmetry that each figure has.a. squareb. regular octagonc. circle
53. Charlie states that the number of degrees of rotational symmetry for a regular hexagon is always a multiple of 60o (0o, 60o, 120o, 180o, …). Is Charlie correct? Use mathematics to justify your answer.
71. Graph the points on the coordinate plane.What kind of quadrilateral is ABCD? Use mathematics to justify your answer.
72. Points are three vertices of a parallelogram.
a. How many parallelograms can be formed using these three points?
b. Give the coordinates of the fourth vertex of the other parallelograms.
73. A triangle has vertices . Use slopes to determine whether the triangle is a right triangle. Justify your answer using mathematics.
74. In a coordinate plane, point A has coordinates and point B has coordinates
. What are the coordinates of the midpoint of ?
75. For each figure below, determine which congruence postulate or theorem can be used to prove the triangles congruent. If the triangles cannot be proven congruent, state that fact.
76. Given: is the perpendicular bisector of .Prove:
77. Given:
Prove:
78.
Given:
Prove:
79. Quadrilateral PQRS has diagonals and that intersect at point T. For the conditions given below, state whether the quadrilateral is a rhombus, rectangle, parallelogram, or none of these figures.