Geometry Quarter 1 Test - Study Guide.

Transcription

1 Name: Geometry Quarter 1 Test - Study Guide. 1. Find the distance between the points ( 3, 3) and ( 15, 8). 2. Point S is between points R and T. P is the midpoint of. RT = 20 and PS = 4. Draw a sketch to show the relationship between the specified segments. Find ST. 3. Find AB and BC if BC = 7x 13, AB = 4x + 26, B is the midpoint of. 4. Find the coordinates of the midpoint of the segment with the given pair of endpoints: J(6, 6); K(2, 4) 5. Find the measures of and if bisects. The measure of is. Draw a sketch that shows the given information. 6. In the figure shown, m AED = 117. True or False: and are adjacent angles and. 7. a. Name a pair of vertical angles in the figure: b. Name an angle supplementary to in the figure. 8. Complete the table. n nth number 1 3 5??? 9. Identify the hypothesis and conclusion of the statement. If yesterday was Saturday, then tomorrow is Monday. 10. "If, then I will go to the game." What is the underlined portion called in this conditional statement? 11. Is the statement true or false? Explain your reasoning. Perpendicular lines always intersect at right angles. 12. Refer to the following statement: Two lines are perpendicular if and only if they intersect to form a right angle. A. Is this a biconditional statement? B. Is the statement true? 13. Write the converse of the true statement and decide whether the converse is true or false. If the converse is true, combine it with the original statement to form a true biconditional statement. If the converse is false, state a counterexample: If four points are not coplanar, then they are not collinear.

2 14. True or False: True biconditional statements make good definitions. 15. If points P, Q, and X are collinear, is it true that PQR and XYZ must be coplanar? Justify your answer. State the postulate indicated by the diagram Identify the property that makes the statement true. If m 1 + m 2 = 25 and m 1 = 9, then. 19. True or False: If two angles are complements of the same angle, then they must be equal in measure and 2 are complementary, and 2 and 3 form a linear pair. If m 1 =, what is m 3? Explain your reasoning. 21. and. If =, what is? Justify your answer. 22. Draw two planes that intersect at. Draw so that it intersects at point J. Are and coplanar? Explain your answer. 23. You and your friend each drew 3 points. Your 3 points lie in only 1 plane, but your friend's 3 points lie in more than one plane. Explain how this is possible. 24. R, S, and T are collinear. S is between R and T. RS = 2w + 1, ST = w 1, and RT = 18. Use the Segment Addition Postulate to solve for w. Then determine the length of 25. If AB = 17 and AC = 32, find the length of.

3 26. On a certain farm, individual crops are laid out in rectangles that are 60 feet north and south, and 40 feet east and west. How far would you have to walk to get from the shed (S) to the well (W) if you did not step on any crops? How far would it be if you walked diagonally across the crops? 27. Find the length of 28. a. What are the approximate lengths of and? b. Find the midpoint of each segment. What is true about the midpoints? 29. m SQR = ( ) and m PQR = ( ) and m SQP = 70. Find m SQR and m PQR. 30. Open-ended: Write three facts you observe in the figure below. 31. In the figure (not drawn to scale), bisects, and. Solve for x and find 32. Which is not a possible value for y in the figure below? a) 96 c) 141 b) 76 d) 89

4 33. Give a counterexample to the following conjecture. All mammals cannot fly. 34. Use inductive reasoning to find the next two numbers in each pattern. 2, 3, 5, 8,, 35. Write an example of each type of statement. a. a true statement with a false converse b. a true statement with a true converse c. a false statement with a false converse d. a false statement with a true converse 36. Given that: i. Tawana bought a new computer. ii. All computers depreciate in value. What conclusion can be logically deduced? 37. Use deductive reasoning to show that the product of two even numbers is even. 38. For each set of true statements, make a valid conclusion, if possible. If none can be made, write "no valid conclusion." a. If a triangle has two acute angles, then the third angle may be obtuse. Triangle ABC has two acute angles. b. If I go to school, I'll ride the school bus. If I ride the school bus, I'll sit next to Kerry on the bus. I went to school. c. If a polygon is a regular, then it is convex. Polygon RSTU is convex. Write a two-column proof. 39. Given:, is supplementary to, and is supplementary to 40. Given: are vertical angles; form a linear pair are supplementary angles 41. Given: bisects

5 42. Sketch an example of lines intersected by a transversal. Identify a pair of : alternate interior angles, corresponding angles, consecutive interior angles and alternate exterior angles. 43. Is the statement true or false? Explain your reasoning. Intersecting lines are always perpendicular. 44. Write the converse of the true statement and decide whether the converse is true or false. If the converse is true, combine it with the original statement to form a true biconditional statement. If the converse is false, state a counterexample: If two lines are parallel, then they never intersect. 45. Use the figure to name a pair of: parallel lines, skew lines, perpendicular lines, parallel planes and perpendicular planes. 46. Find m 1 in the figure below. PQ and RS are parallel. 47. True or False: If two parallel lines are intersected by a transversal, then consecutive interior angles are complementary. 48. Given: Lines q and r are parallel. Transversal t intersects lines q and r. are supplementary. 49. In the figure below, if l and k are parallel lines, what is the value of x and y?

6 50. Use the given angle measures to decide whether lines a and b are parallel., 51. Calculate the slope of the line. Does it matter which points are used? Why? 52. Writing: Explain the difference between a horizontal line and a vertical line in terms of slope. Give an example of an equation for each type of line. 53. A line L1 has slope -1. State whether the line that passes through ( 3, 2) and (5, 10) is parallel or perpendicular to line L Decide whether Line 1 and Line 2 are parallel, perpendicular, or neither. Line 1 passes through (10, 7) and (13, 9) Line 2 passes through ( 4, 3) and ( 1, 5) 55. Find the slope of the line through the points ( 1, 3) and ( 1, 7). 56. Write the slope-intercept form of the equation of the line passing through the point ( 2, 5) and parallel to the line 57. Write the slope-intercept form of the equation of the line passing through the point (5, 4) and perpendicular to the line 58. Write an equation in slope-intercept form 59. Line l passes through (1, 1) and ( 2, 8). of the line shown. Graph the line perpendicular to l that passes through ( 2, 2). 60. Find the shortest distance between y = x 1 and y = x + 3.