Geometry Final Review

Transcription

1 Name: ate: 1. In the accompanying diagram, lines a and b are parallel, and lines c and d are transversals. Which angle is congruent to angle 8? 2. Which geometric principle is used to justify the construction below?. line perpendicular to one of two parallel lines is perpendicular to the other.. 6 B. 5 C B. Two lines are perpendicular if they intersect to form congruent adjacent angles. C. When two lines are intersected by a transversal and alternate interior angles are congruent, the lines are parallel.. When two lines are intersected by a transversal and the corresponding angles are congruent, the lines are parallel. 3. In the accompanying diagram, parallel lines B and C are intersected by EF at G and H, respectively. If m GH = 5x and m CHG = x + 12, find the value of x. page 1

2 4. In the accompanying diagram, BC E, m FE = 25, m FE = 130, and m B = x. What is the value of x? 8. In isosceles triangle OG, the measure of the vertex angle is three times the measure of one of the base angles. Which statement about OG is true?. OG is a scalene triangle. B. OG is an acute triangle. C. OG is a right triangle.. OG is an obtuse triangle. 5. Two complementary angles are in the ratio 8 : 1. The number of degrees in the larger angle is. 10 B. 20 C Two angles are supplementary, and the measure of one angle is three times the measure of the other. Find the measure of the smaller angle. 7. If the angles of a triangle are represented by x, 3x + 20, and 6x, the triangle must be. obtuse B. right C. acute. isosceles page 2

3 9. Which diagram represents a correct construction of equilateral BC, given side B?. 11. If the number of degrees in a base angle of an isosceles triangle is four times the number of degrees in the vertex angle, what is the number of degrees in a base angle of the triangle? B. 12. In BC, the measure of is 50 and the measure of an exterior angle at vertex B is 125. Which is the longest side of the triangle? C. 13. In the accompanying diagram, C is an exterior angle of BC, m = 3x, m C = 5x, and m B = 50. What is the value of x?. 25. B. 30 C If two sides of a triangle have lengths 4 and 9, then the length of the third side may be any number. greater than 4 but less than The length of a side of an equilateral triangle is represented by 2x 1. If the perimeter of the triangle is 21, what is the value of x? B. greater than 5 C. less than 13. greater than 5 but less than 13 page 3

4 15. Which set of numbers could represent the lengths of the sides of a triangle? 19. Solve for the positive value of x: x 2 5x 24 = 0. {9, 16, 20} B. {8, 11, 19} C. {3, 4, 8}. {11, 5, 5} 16. If M(2, 5) is the midpoint of B and the coordinates of are (4, 7), what are the coordinates of B? 20. When 5 20 is written in simplest radical form, the result is k 5. What is the value of k?. 20 B. 10 C (1, 6) B. (2, 12) C. (8, 6). (8, 3) 17. What is the distance between points R(5, 7) and S(2, 3)? 21. If 84 is simplified to a b such that a and b are integers, what is the value of a?. 25 B. 33 C What is the solution set of the equation x 2 3x 10 = 0?. (5, 2) B. (5, 2) 22. If MNP = VWX and PM is the shortest side of MNP, what is the shortest side of VWX?. XV B. WX C. VW. NP C. (5, 2). (5, 2) page 4

5 23. s shown in the diagram below, C is a median of BC. 25. What is the slope of the line perpendicular to the line represented by the equation 2x + 4y = 12?. 2 B. 2 C Which statement is always true?. = B B. C = C. C = CB. BC = C 24. In the diagram below, under which transformation is B C the image of BC? 26. Using a compass and straightedge, construct a line perpendicular to line lthrough point P. [Leave all construction marks.]. 2 B. r xaxis C. r yaxis. (x, y) (x 2, y) page 5

6 27. Triangle BC has vertices (5, 1), B(1, 4), and C(1, 1). State and label the coordinates of the vertices of B C, the image of BC, following the composite transformation T 1,1 2. [The use of the set of axes below is optional.] 29. In the diagram below, EC = BE. Which statement is not always true?. C = B B. CE = E C. EC = EB. CE = BE 30. In the diagram of PQR shown below, PR is extended to S, m P = 110, m Q = 4x, and m QRS = x 2 + 5x. 28. The measures of the angles of a triangle are in the ratio 2 : 3 : 4. In degrees, the measure of the largest angle of the triangle is. 20 B. 40 C What is m Q?. 44 B. 40 C page 6

7 31. s shown in the diagram below, S is a diagonal of trapezoid STR, R ST, m TS = 48, m RS = 47, and m RS = Given: BE and intersect at point C BC = EC C = C B and E are drawn Prove: BC = EC etermine and state the longest side of ST. 32. In the diagram below of isosceles BC, the measure of vertex angle B is 80. If C extends to point, what is m BC?. 50 B. 80 C Using a compass and straightedge, construct the perpendicular bisector of side R in RT shown below. [Leave all construction marks.] 33. Triangle B C is the image of BC after a dilation of 2. Which statement is true?. B = B B. BC = 2(B C ) C. m B = m B. m = 1 2 (m ) page 7

8 36. Quadrilateral HYPE has vertices H(2, 3), Y(1, 7), P(2, 7), and E(2, 4). State and label the coordinates of the vertices of H Y P E after the composition of transformations r xaxis T 5,3. [The use of the set of axes below is optional.] 38. The sum of the interior angles of a polygon of n sides is. 360 B. C. (n 2) n (n 2) 180 n 39. line that passes through the points whose coordinates are (1, 1) and (5, 7) is dilated by a scale factor of 3 and centered at the origin. The image of the line 37. In the diagram below, LMO is isosceles with LO = MO.. is perpendicular to the original line B. is parallel to the original line C. passes through the origin. is the original line If m L = 55 and m NOM = 28, what is m N?. 27 B. 28 C page 8

9 40. In the diagram below, rectangle BC has vertices whose coordinates are (7, 1), B(9, 3), C(3, 9), and (1, 7). 41. In BC, B is the perpendicular bisector of C. Based upon this information, which statements below can be proven? I. II. B is a median. B bisects BC. III. BC is isosceles.. I and II, only B. I and III, only C. II and III, only. I, II, and III Which transformation will not carry the rectangle onto itself?. a reflection over the line y = x B. a reflection over the line y = x + 10 C. a rotation of 180 about the point (6, 6). a rotation of 180 about the point (5, 5) page 9

10 42. Given: BC, EC, BE with BE = CBE, and E = CE Prove: BE is the perpendicular bisector of C Fill in the missing statement and reasons below. Statements 1. BC, EC, BE with BE = CBE and E = CE 2. B = B B and E are supplementary. BC and CE are supplementary. 1. Given Reasons 3. Linear pairs of angles are supplementary Supplements of congruent angles are congruent. 5. B = CB 5. S 6. = C, B = CB BE is the perpendicular bisector of C 7. page 10

11 Problem-ttic format version c Educide Software Licensed for use by Michael Pagan Terms of Use at 1/3/ C B B C B correct construction is drawn showing all appropriate arcs. 27. (11, 1), B (3, 7), and C (3, 1) C B ST, and correct work is shown. C [proof] [activity] H (7, 0), Y (6, 4), P (3, 4), and E (3, 1) C B

12 Teacher s Key Page C [task]