1stQuarterReview.nb If two parallel lines are cut by a transversal, 2. If point B is between points A and C, then AB + BC =.
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1 1stQuarterReview.nb 1 Geometry (H) Review: First Quarter Test Part I Fill in the blank with the appropriate word or phrase. 1. If two parallel lines are cut by a transversal,. 2. If point B is between points A and C, then AB + BC =. 3. If AOC is a straight angle and B is any point not on AC õ, then m AOB + m BOC =. 4. A line contains at least points, a plane contains at least points not all in one line, and space contains at least points not all in one plane. 5. Through any two points there is. 6. The three undefined terms used in plane geometry are. 7. A statement assumed to be true is known as a. 8. The set of all points is known as. 9. Points that lie on the same line are called.
2 1stQuarterReview.nb A point that divides a segment into two congruent segements is known as. 11. lines are two lines that intersect to form right angles. 12. An angle whose measure is 180 is known as. 13. The process of making a geometric figure with a straightedge and compass is known as. 14. Non-parallel, non-intersecting lines are called. 15. Two, distinct, collinear rays with the same endpoint are called. Part II Fill in the blank with the appropriate word or phrase. 1. A statement in if-then form is known as a. 2. The converse of the statement "if p, then q" is. 3. The inverse of the statement "if p, then q" is. 4. The contrapositive of the statement "if p, then q" is. 5. If two statements are logically equivalent it means they have the same. 6. The converse of a statement is logically equivalent to the.
3 1stQuarterReview.nb 3 7. List the five parts of a proof in two-column form. (A) (B) (C) (D) (E) 8. Given the statement "All right angles are congruent" write (A) The statement in if-then form. (B) The converse of the statement. (C) The inverse of the statement. (D) The contrapositive of the statement. Part III 1. Describe, using correct terminology, the procedure for constructing the perpendicular bisector of a segment. 2. Describe, using correct terminology, the procedure for bisecting an angle.
4 1stQuarterReview.nb 4 3. State the three undefined terms which are accepted as intuitive ideas in Geometry. State the word or phrase that is defined in each of the problems below. 4. Points all in one plane. 5. The set of all points. 6. Points all in one line. 7. Non-parallel, non-intersecting lines. 8. A conclusion reached by using inductive reasoning. 9. The point that divides a segment into two congruent segments. 10. A line, segment, ray or plane that intersects a segment at the point defined in # Segments with the same length. 12. The figure formed by two rays with the same endpoint. 13. An angle whose measure is between 90 and Two angles with a common vertex and a common side but no common interior points. Answer the following questions about postulates. 15. What is a postulate (or axiom)? 16. According to the Segment Addition Postulate if B is between A and C what must be true?
5 1stQuarterReview.nb According to the second part of the Angle Addition Postulate if AOC is a straight angle and B is any point not on AC õ, the m AOB + m BOC =? 18. If two points are in a plane what can you conclude about a line that contains the points? 19 What can you conclude about the intersection of two distinct planes? 20. Complete the following postulate: If two parallel lines are cut by a transversal, then... Complete with always, sometimes, or never to make a true statement. 21. Intersecting lines are coplanar. 22. Two planes intersect in exactly one point. 23. Three points are coplanar. 24. A line and a point not on a line are coplanar. 25. Four points are coplanar. 26. Two lines meet in more than one point. 27. AB øøö 28. AB øøö and BA øøö and øø AC ö are the same ray. are the same ray. 29. AX and XA are the same segment. 30. TQ õ õ and QT are the same line. 31. Skew lines are coplanar.
6 1stQuarterReview.nb 6 2y + 1 y - 1 A B C If AC = 45, find the value of each of the following. 32. y 33. AB 34. BC D E F A B C Find the measure of each angle below. 35. EBF 36. EBA 37. DBE 38. DBC 39. ABF 40. DBF
7 1stQuarterReview.nb 7 Find the measure of each angle. C D J K M B 41. CDM 42. KDM 43. JDK 44. JDM 45. CDB 46. CDK Part IV Questions 1-4 refer to the digram below. Note that lines a and b are parallel. t a b 1. 3 and 5 can be classified as
8 1stQuarterReview.nb and 6 can be classified as 3. 3 and 6 can be classified as 4. If m 1 = 120, find the measures of the angles listed below. (A) 2 (B) 4 (C) 6 (D) 7 (E) 5 (F) 8 Determine whether the following statements are TRUE or FALSE. 5. If two angles are congruent and supplementary, each is a right angle. 6. All right angles are congruent. 7. Two vertical angles may be complementary. 8. If a line is perpendicular to one of two parallel lines then it is perpendicular to the other line. 9. The statement "If B, then A" is an example of the reflexive property. Questions refer to the following: P Q R S T V 10. From the figure illustrated above, name a pair of corresponding angles. 11. From the figure illustrated above, name a pair of alternate interior angles.
9 1stQuarterReview.nb From the figure illustrated above, name a pair of same-side interior angles. Questions refer to the following: D 3 C A B 13. Name the segments, if any, that are parallel if Name the segments, if any, that are parallel if Name the segments, if any, that are parallel if DCB and 6 are supplementary. 16. Two angles are complementary. The larger angle exceeds twice the smaller angle by 15. Find the measure of each angle. 17. Two angles are supplementary. If the measure of one of the angles is z +20 degrees, find the measure of the other angle in terms of z.
10 1stQuarterReview.nb Write the converse, inverse, and contrapositive of the conditional below and determine the truth value of each statement. Converse ö Truth value Inverseö Truth value If ED lives in Nashville, then he lives south of Canada. Contrapositiveö Truth value Questions refer to figure below. Use the given information to determine which lines, if any must be parallel. If any lines are parallel, justify with a postulate or theorem m 7 = 70, m 9 = is supplementary to
11 1stQuarterReview.nb Complete the following proof. t a 3 2 b 1 Given: a»» b Prove: 3 Statements Reasons Given Vert. 's Part V Fill in the blank with the appropriate word or phrase. 1. Another name for an if-then statement is a. The part after the if is the and the part after the then is the. 2. When you determine whether a conditional is true or false you determine its. 3. The of a conditional interchanges the hypothesis and conclusion.
12 1stQuarterReview.nb When a conditional and its converse are true, you can combine them as a. 5. The of a statement has the opposite meaning. 6. The of a conditional negates both the hypothesis and the conclusion. 7. The of a conditional interchanges and negates both the hypothesis and the conclusion. 8. The congruent sides of an isosceles triangle are the and the third side is the. 9. The congruent sides of an isosceles triangle form the angle; the other two angles are the angles. 10. Given the conditional statement "If p, then q" write each of the following: A) the converse B) the inverse C) the contrapositive 11. The segment connecting the midpoints of two sides of a triangle is called a. 12. A is a set of points that meet a stated condition.
13 1stQuarterReview.nb 13 Complete each of the following theorems. 13. If two sides of a triangle are congruent, then 14. The bisector of the vertex angle of an isosceles triangle is 15. If a triangle is equilateral, then 16. If a triangle is a right triangle, then the acute angles are 17. If two angles of one triangle are congruent to two angles of another triangle, then 18. All right angles are 19. If two angles are congruent and supplementary, then 20. If a segment joins the midpoints of two side of a triangle, then the segment is 21. The sum of the lengths of any two sides of a triangle is 22. If two sides of a triangle are not congruent, then the larger angle 23. If a point is on the perpendicular bisector of a segment, then it is equidistant from 24. If a point is on the bisector of an angle, then it is equidistant from êêêêê êêêê êêêêê 25. Find the value of x given that R, S, and T are midpoints of AC,BC, and AB respectively and the perimeter of DABC = 120. A T 2x + 2 4x R x + 2 S C B
14 1stQuarterReview.nb Find the value of the variables. a c b List the angles of DXYZ from smallest to largest given XY = 10, YZ = 11, and XZ = Write an inequality to represent the range of values for z, the third side of a triangle, if the lengths of the other two sides are 8 and 12.
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