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Geometry Review for Fall Semester Exam 2014
1. Write the equation of a line with y-intercept of 5 and a slope of ¾. Put your equation in standard form.
2. Write the equation of a line perpendicular to y = 1/4x - 8 and through the point (5,6)
3. Write the equation of a line parallel to y = -2/3x + 5 and through the point (2, 4).
4. Write the equation of a line containing the points (2, 1) and (3, 4).
5. Find the y and x intercepts of the following Standard Form equation 2x + 3y = 5.
6. Write the equation of a line with y-intercept of -4 and a slope of 1/2. Put your answer in standard form.
7. Write the equation of a line perpendicular to y = 2\3x - 6 and through the point (3,4). Write your answer in slope - intercept form.
8. Write the equation of a line parallel to y = 3/4x + 4 and through the point (1,3). Write your answer in point – slope form.
9. Write in standard form the equation of a line containing the points (-3,5) and (2, 8).
10. Find the y and x intercepts of the equation 3x + 4y = 12.
11. Refer to the number line above to find each measure.
a) CD=____ b) BF=____ c) CF=____d) EB=____ e) ____f) ____ g) EF + DE = ____
12. The Segment Addition Postulate states that if D is between B and F then BD + ________ = BF 13. Give the coordinate of the midpoint of each segment on the number line above.
a) b) c)
14. Refer to the coordinate plane to find each measure. Round to two decimals. Show work.
a)BA = ___ b) ED = ____ c) CD = ____d) AC = _____
15. Using the same coordinate plane, find the coordinates of the midpoint of each segment.
Show work. a) b)
16. If D is the midpoint of , give the coordinates of F.
17. If E is the midpoint of , give the coordinates of G.
18. Find the length of .
19. In the figure at right, and are opposite rays, and bisects .
a) Name two congruent angles. b) Name 3 angles that have U as a vertex.
c) If and , what is the measure of ?
d) If , and ,find Show work.
e) Find if , and . Show work.
20. The measure of an angle is three times the measure of its supplement. Find the measures of both angles. Show work
21. and are complementary. Find and if and.Show work.
22. Use the picture on the right to answer the following questions. Box your answers. Show work.
a) What is the measure of 3? b) If the m 4 = 3x + 16 and the m 5 = 2x + 24, find x.
c) Using the information from the previous problem, find the m 2.
d) 1 is 10 more than 4 times the measure of 2. Find the measure of 1 and 2.
Determine if the two triangles are similar. Show work.
If so, write the similarity statement and the reason why (AA~, SSS~, SAS~)
BABCE80ºD63º37º23. by __________ 12.88.414.4JKLF24. by__________
25. Similar polygons have corresponding sides that are ______ and corresponding angles that are _______.
26. True/False a) All congruent figures are similar. b) All similar figures are congruent. c) All circles are similar. d) All squares are similar.
27. If a 90 foot tall tree casts a 54 foot shadow, how tall is a house that casts a 10 foot shadow? ____________ 28. Use diagram below to find the values of: 29. In ∆EFG below, ║. 30. In ∆EFG, ║ . Solve for x = ____
a) x = ____ b) y = ____ c) z = ______ If EI = 8, IF = 4, EH = 5, find GH.
IF HI = 10 then what is the perimeter
of triangle GLF.
31. Use figure below to solve for x = ________ 32. A surveyor standing at point T figures that a river is 98 ft wide. If the surveyor plans to
cross the river at point W, how far will he have to walk?
=33. A basketball player made 12 free throws in his last 36 attempts. How many free throws would the player expect to make in 78 attempts?
34. Solve for x.9 12 35. Solve for x. 4 2_ 24 x x x - 2
Use the following diagram to determine which lines are parallel and which line is the transversal for the following angle pairs.
7 and 13
39. m parallel n angle 3 = 2x+10 angle 9 = 8x+90 find x.
40. m parallel n angle 8=3x+5 angle 13 = 2x-1.
The triangle ABC is a right triangle and line DE is parallel to line BC. 44. If line l1 and line l2 are parallel, Find x.
Answer the following questions using this triangle. SHOW YOUR WORK.
41. Find z
45. Write the converse, inverse, and contrapositive of the statement, “If a triangle is equilateral, then it is equiangular”.
46. Identify the hypothesis and conclusion of the statement, “If the weather is good, then a picnic is enjoyable.”
47. Write a biconditional from the following two conditional statements.
If a quadrilateral is a parallelogram, then its opposite sides are parallel.
If the opposite sides of a quadrilateral are parallel, then it is a parallelogram
48. Name 3 lines that are skew to line GH
49. Name 2 points that are coplanar with B
50. Name the fourth point in Plane ABH
51. What is the intersection of Plane ACGE and Plane ABDC?
H52. Find the measure of a base angle of an isosceles triangle if the vertex angle measures 38° and the two congruent sides measure 21 units each? 53. If mH = (7y-3)0 and mB = (3y+13)0. Find measure of angle O. 54. Find the degree measure of angle x
55. Find the measure of the sum of interior angles of a 15-gon
56. Find the measure of each exterior angle of a regular polygon with 18 sides.
57. The sum of the interior angles of a convex polygon is 16200. Find the number of sides.
58. Find the measure of one interior angle of a regular polygon with 21 sides.
59. Using figure at right, find x.
60. Reflect a triangle with vertices , , and across the x-axis. Find the coordinates of the new image. 61. Reflect a figure with vertices (2, 1), (6, 3), (7, 6) and (4, 6) across the y-axis. Find the coordinates of the new image.
62. Dilate a triangle with vertices , , and with a scale factor of 2 centered at the origin. Find the coordinate of the new image.
63. Find the coordinates of the image of the point (3, 4) when it is reflected across the line y = 1.
64. Find the coordinates of the image of the point (–4, 2) when it is reflected the line y = –4.
65. Rotate ∆RST with vertices R(–1, 4), S(2, 1), and T(3, –3) by 90° about the origin.
66. Rotate ∆ABC with vertices A(2, 8), B(5, 7), and C(1, 2) by 90° about the origin.
67. Reflect Δ JKL with vertices J(2, 2), K(4, –5), and L(–1, 6) across the y-axis and then reflect the image across the x-axis. Describe a single transformation that moves the triangle from its starting position to its final position.
68. has vertices A(3, –1), B(4, 3), and C(2, 1). Rotate 90° about the origin and then reflect it across the x-axis. Give the image points of the vertices.
69. Justify why the following triangles are congruent.
70. If PRD MJB, then DP is congruent to ______?
71. BCD EFG and CD = 9x+2, FG = 3x + 20, what is the length of CD?
72. If CAT RED, mD = 50, and mA = 45, what is the measure of R?
73 GIVEN: ST UR; 74. What postulate/theorem can we use to Prove the triangles below are congruent?
PROVE: TSR RUT
76. In the diagram below, MRO ______ by ____
RMOQPN75. GIVEN: JF EK
JF bisects EK
PROVE: 1 2
77. In the figure below, if MNOP is an isosceles trapezoid and MO = NP, then by ________?
78. Given ABC KLM, if m find
a) the value of x
79) Which the following statement(s) is/are incorrect?
a) All equilateral triangles and squares are similar.
b) All right triangles with the same hypotenuse and a leg are similar and congruent.
c) All congruent figures are similar with each other.
d) Two triangles are congruent if SSS, SAS, SSA, AAS, ASA or HL theorems/postulates are fulfilled.
e) Two rectangles are always congruent if they have congruent corresponding sides.
f) Reflections, translations and rotations always give congruent figures.
80) Given and , ΔTXA ΔSXE by ___ versal
40. m parallel