DO NOT LOSE THIS REVIEW! You will not be given another copy.

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1 Geometry Fall Semester Review 2011 Name: O NOT LOS THIS RVIW! You will not be given another copy. The answers will be posted on your teacher s website and on the classroom walls. lso, review the vocabulary from all units! Finally, review all your old tests and quizzes! 1.1: oints, Lines, lanes, and Logical Reasoning 1. Refer to the figure on the right. a. Write 3 other names for line l. b. Name 4 coplanar points. c. Name 4 noncoplanar points. d. Name 3 collinear points. e. Name 3 noncollinear points. f. Write another name for plane. g. Name a pair of opposite rays. h. Name a pair of parallel lines. i. Name a pair of intersecting lines. j. Name a pair of skew lines. k. Name the intersection of planes and GF. T F G l m 2. Find m if bisects, 3. Find the value of x. m 1 = 5x 11, and m 2 = 3x + 5. Name the angle pair and explain their relationship. L 1 2 K (x + 5) (x - 3) 4. Find the value of x. 5. Find the value of x. Name the angle pair in 2 ways Name the angle pair and explain their relationship. (l p and s ) and explain their relationship. N M O G 3x (80 - x) (12x + 4) 4x I J H J 6. Refer to the figure to the right. JK = 2x + 7. KL = 6x 5. a) Find x if JL = 12x 12. b) Find x if K is the midpoint of JL. 1 K N M 7. Write the converse, inverse, and contrapositive of the following conditional. Then determine their truth values. "If m 1 = m 2, then 1 and 2 are vertical angles." onverse: Truth value: Inverse: Truth value: ontrapositive: Truth value: L 1

2 8. Write the following statement as a conditional: "n odd integer is not divisible by 2." If-then form: Truth value: Write the converse: Truth value: Is the converse true or false? If false, give a counterexample. If both the converse & original conditional are true, combine them as a biconditional. 9. "If two integers are odd, then their sum is even." Is this conditional statement true/false? Write the converse: Truth value: Is the converse true or false? If false, give a counterexample. If both the converse & original conditional are true, combine them as a biconditional. 1.2: ythagorean Thm, istance, Midpoint, arallel Lines & ngle Relationships 10. etermine the length of M. 11. The figure below shows an isosceles triangle on top of a rectangle. What is the length of one leg of the triangle? 24 ft 12. Find the length of the segment with endpoints (1, 4) and (-2, 7). 13. Find the midpoint of the segment with endpoints (5, -2) and (-1, 8). 14. coordinate grid is placed over a map of Hightower High School. The front door is located at (9, 9) and the back door is located at (-2, 1). a) You are standing halfway between these doors. What are your coordinates? b) How far apart are the doors, to the nearest unit? 15. ircle Q has a diameter WY. oint W is located at (3, -2) and point Y is located at (-5, -6). a) What are coordinates of Q, the center of the circle? b) What is the length of the radius of the circle? 16. Refer to the figure on the right. Identify the name of the angle pair. Find the angle measures if m 8 = 110. a) 1 and 8 m 1 = m 8 = 110 b) 6 and 8 m 6 = m 8 = 110 l m n c) 7 and 12 m 7 = m 12 = d) 10 and 11 m 10 = m 11 = p 2

3 17. Use angles relationships, parallel lines, triangles, & polygons to solve for the variables in the diagram. a = b = c = d = e = f = g = h = k = m = n = p = r = s = u = Optional: t = v = 1.3: pplications of Slope & quations of Lines, Translations and Reflections 18. Refer to parallelogram to answer the following questions. a) What is the equation of in point-slope form? y suur b) What is the slope of a line perpendicular to? K c) What is the equation of? d) What is the slope of a line perpendicular to? x 19. Given line r: 3x + 8y = -16 a) What is the slope and y-intercept of line r? b) Write an equation of a line that contains (-1, 5) and is parallel to line r. c) Write an equation of a line that contains (0, 4) and is perpendicular to line r. 20. Find the slope of the line that contains (0, 3) and (8, 7). 21. Find the slope of a line parallel to the line passing through (5, -1) and (3, 1). 22. Find the slope of a line perpendicular to the line passing through (-2, 3) and (1, -2). 3

4 Find the equation of the line passing through the given points. (Hint: use the 2 points to find the slope, then plug in a point and the slope into point-slope form: y y 1 = m(x x 1 ). Then solve for y = mx + b form if necessary). 23. (1, 5), (-3, 4) in point-slope form 24. (0, -2), (-1, -3) in slope-intercept form 25. (-2, 4), (6, -3) in slope-intercept form 26. Graph with and, and its image under the translation right three units and up two units. Write the mapping notation of this translation: (x, y) How is slope affected by a translation? 27. Then graph the reflection of ' ' across the y-axis. Write the mapping notation of this reflection: (x, y) How is length affected by a reflection? 2.1: ngles, Triangles, olygons, Rotations and Symmetry The measure of the vertex angle 3x 4 x - 3 of an isosceles triangle is 100. What is the measure of each base angle? 5x x lassify each triangle by its angles (acute, obtuse, right) N by its sides (scalene, isosceles, equilateral). 31. G, with m = 90, G = 4, = I, with I = 8, I = 18, = 15. (HINT: use the ythagorean onverse: is c 2 = or < or > a 2 + b 2?) 33. WHO, with m W = 110, WH = WO = Find the m H and m O of the triangle in the previous question a) Find the sum of exterior angles of a regular 15-gon. b) Then find the measure of one exterior angle. 36. a) Find the sum of interior angles of a regular polygon with 15 sides. 37. Find above. b) Then find the measure of one interior angle. The diagram is not to scale Graph with and. Find the images of and and the mapping notation under the following counterclockwise rotations: a) 90 : (x, y) How is slope affected by a 90 rotation? a) 180 : (x, y) How is slope affected by a 90 rotation? a) 270 : (x, y) How is slope affected by a 90 rotation? 4

5 2.2: Ratios, roportions, Similarity, and ilations 39. etermine the scale factor for the dilation on the right. 40. What is an isometry? Which of the following transformations are isometries? a. Translation b. Reflection c. Rotation d. ilation e. istortion 41. basketball player made 36 free throws in 16 games. If the basketball player plays 28 games total with the same ratio, predict the number of free throws he made. 42. The polygons are similar, but not necessarily drawn to scale. Find the values of x, y, and z, and the perimeter of the larger polygon. lso find the scale factor from the smaller polygon to the larger polygon. 130 z 43. etermine whether the pair of triangles is similar. If so, complete the similarity statement and give the reason (name the triangle similarity theorem:, SSS, or SS): F by F etermine whether the two figures on the right are similar, congruent or neither. xplain your answer. 30 F 45. Find and. xplain why these triangles are similar (name the triangle similarity theorem). 46. omplete the similarity statement: by. Find x =, =, and =. If = 4, find the length of =. What is the special segment name for? 47. Find x to the nearest tenth Solve for x. (Hint: draw the two triangles separately and label.) )) x 6.7 x )) 11.6 Not drawn to scale

6 2.3: ongruence in Triangles, including Special Segments 49. Name the 5 postulates than can be used to prove TRINGL ONGRUNY. omplete each congruence statement. Mark all information on triangles. 50. Δ HM Δ by Mark the following given information on triangles: M MH, T TH, MH T Justify re- Geometry: instead of completing the "Justify" parts, write two-column proofs for questions # T M H 51. Δ Δ by Mark all information on triangles is the midpoint of both and. Justify 52. Δ LK Δ by Mark the following given information on triangles: L bisects KLO, m KL = 90 Justify K O xplain why L is an altitude of LKO. L re-: omplete this proof for question #52. Statements Reasons _ Given KL OL m KL = 90 m KO = 180 Given m KL + m OL = m KO Substitution. of. m OL = 90 KL and OL are right ef. of Right ngles KL OL Reflexive. of. LK LO LK LO LKO is isosceles 53. If M is a perpendicular bisector of GO, find x = y = MO = m MO= 54. If is a median, find x = = 3x - 10 x + 4 2x If RS is an angle bisector, find x = m RST = (x - 5) (3x - 25) U (8x + 15) R S T G (4x + 10) 8y M 10y - 8 O 6