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Name __________________________________________ Final Exam Date _______________________ Geometry Final Exam Review ο· The final exam covers all sections taught in class from Chapters 1 through 13. ο· There are 50 multiple choice questions and 6 open-ended questions marked with **. 1) ** Find the distance and midpoint between between the points (7, 3) and (-2, -5). (Chapter 1) 2) Determine whether each statement is always, sometimes, or never true. (Chapter 2) A. Two angles that are supplementary form a linear pair. B. If B is between A and C, then π΄πΆ + π΄π΅ = π΅πΆ. C. If two lines intersect to form congruent adjacent angles, then the lines are perpendicular. 3) Find the measure of each numbered angle, and name the theorems that justify your work. (Chapter 2) 4) Find the measure of each numbered angle, and name the theorems that justify your work. (Chapter 2) 5) ** Use the diagram to the right. (Chapter 2) Μ Μ Μ Μ . a) Find the length of π΄πΆ Μ Μ Μ Μ , what is the probability that it is on π΅πΆ Μ Μ Μ Μ . b) If a point is randomly chosen on π΄πΆ 6) Μ Μ Μ Μ and Μ Μ Μ Μ π»π½ πΈπΊ are parallel. (Chapter 3) a) If πβ πΈπΉπ· = 2π₯ + 1 and πβ π»πΌπΎ = 130, what is the value of x? b) What theorem proves that β πΊπΉπΌ and β π½πΌπΎ are congruent? 7) Find the slope of the line parallel to 4π₯ β 3π¦ = 2. (Chapter 3) 8) If πβ πΎπΌπ½ = 60, πβ πΈπΉπ· = 5π¦, and πβ πΌπΉπΊ = 5π₯ β 10, what is the value of x? (Chapter 3) 9) In the diagram, βπ ππ β βπππ. Find π₯ and π¦. (Chapter 4) 10) ** Complete the proof. (Chapter 4) 11) Determine which postulate or theorem can be used to prove each pair of triangles congruent. If it is not possible to prove them congruent, write not possible. (Chapter 4) a) b) e) g) 12) c) d) f) h) Given: Vertical isosceles triangles; Μ Μ Μ Μ π π bisects Μ Μ Μ Μ ππ; β π β β π Prove: β³ ππ π β Ξπππ (Chapter 4) 13) Determine whether each statement is always, sometimes, or never true. (Chapter 4) a) The Pythagorean Theorem does not apply to right triangles. b) Right triangles can be equilateral. c) The sum of the interior angles of a right triangle is 90 degrees. d) Right triangles are isosceles triangles. 14) List the angles in the triangles from least to greatest. (Chapter 5) 15) Match each term with the correct picture. (Chapter 5) a) Perpendicular bisector b) Angle bisector c) Median d) Altitude 16) If π·πΈ = 14 + 2π₯ and πΊπΉ = 4(π₯ β 3) + 6, find πΊπΉ. (Chapter 6) 17) Determine whether each statement is always, sometimes, or never true. (Chapter 6) a) In a parallelogram, opposite sides are congruent. b) In a parallelogram, opposite angles are congruent. c) In a parallelogram, consecutive angles are complementary. 18) Find the value of x if the vertices of a parallelogram are (β2, β4), (β3, β7, (2, β5), and (π₯, β2). (Chapter 6) 19) Find x in the trapezoid below. (Chapter 6) 20) Determine whether the pair of figures is similar. If so, write the similarity statement and scale factor. If not, explain your reasoning. (Chapter 7) 21) Μ Μ Μ Μ and E is the midpoint of Μ Μ Μ Μ If D is the midpoint of π΄πΆ π΅πΆ , Μ Μ Μ Μ . (Chapter 7) find the length of π΄π΅ 22) ** The two sail boats below form right triangles. Are these two right triangles similar? Show your work and write an explanation to justify your answer. (Chapter 7) 23) 24) 25) (Chapter 7) Μ Μ Μ Μ . (Chapter 7) If ΞMQN~ΞMPO, find ππ (Chapter 7) 26) If ΞLMN~ΞXYZ, find πβ π. (Chapter 7) 27) A wall with a height of 7.5 meter casts a shadow 12 meter long. How high is pole that casts a shadow of 60 meters long? (Chapter 7) 28) Find π₯, π¦, and π§. (Chapter 8) 29) Find the height of the airplane pictured (all measurements in meters). (Chapter 8) 30) If you are standing at point C, how far away are you form the tree? Round to the tenths. (Chapter 8) 31) Name three possible side lengths of a right triangle. (Chapter 8) 32) Write the ratio of cos π½. (Chapter 8) 33) Suppose you're flying a kite, and it gets caught at the top of a tree. You've let out all 100 feet of string for the kite, and the angle that the string makes with the ground (the angle of elevation) is 75 degrees. What is the height of the tree? Round to the tenths. (Chapter 8) 34) An isosceles right triangle has an area of 50 square inches. What is the length of the hypotenuse in inches? (Chapter 8) 35) Find the width of the rectangle. Round to the nearest tenths. (Chapter 8) 36) A kite is being flown and gets caught in the power lines. If the kite string makes a 45 degree angle with the ground and you are standing 10 feet away from the power lines, how long is the kite string? Round to the nearest foot. (Chapter 8) 37) Does a triangle with side lengths 5, 12, and 13 form a right triangle? (Chapter 8) 38) An equilateral triangle has a side length of 5. What is the measure, in inches, of its altitude? Round to the hundredths. (Chapter 8) 39) Find π¦ to the nearest tenth. (Chapter 8) 40) Find the altitude of the right triangle drawn to the hypotenuse. (Chapter 8) 41) Use a calculator to find the measure of angle R to the nearest tenth. (Chapter 8) a) b) 42) ** Use the grid to the right to answer the following questions. (Chapter 9) a) On the grid above, draw a reflection of figure F over the y-axis to form figure Fβ. b) Draw a reflection of figure Fβ over the x-axis to form figure Fβ. c) In the space below, describe another transformation or a set of transformations that would transform figure F to figure Fβ. 43) ** Graph the concentric circles with center at (2,0) and radii of 1 and 3 on the graph below. (Chapter 10) a) Write the standard form of the equation of the equation of the circle for both circles. b) What is the probability that a randomly thrown dart will land inside the smaller circle? 44) The circumference of a circle is 10 feet. If the length of the diameter is double, what is the new circumference, to the closest foot? (Chapter 10) 45) Find the area of each figure. Round to the nearest tenth if necessary. (Chapter 11) a) 46) b) c) A geometric figure is cut up and laid flat, as shown on the right. What geometric figure would most closely resemble the geometric figure put back together? (Chapter 12) 47) Find the volume of each prism or cylinder. Round your answer to the nearest tenth. (Chapter 12) a) 48) b) Point X is chosen at random on Μ Μ Μ Μ π΄πΈ . Find the probability of each event. (Chapter 13) Μ Μ Μ Μ ) a) π(π ππ ππ π΄πΆ b) π(π ππ ππ Μ Μ Μ Μ πΆπ·) 49) Find the area of the UNSHADED region of the circle. (Chapter 13)