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Geometry Mid-Term Exam Review Unit #1 – Unit #6 (2015-16) Name:____________________________________________ Due _____________________ Chapter 1 Topics: Unique Line Assumption Angle Addition Postulate Flat Plane Assumption Segment Addition Postulate Line Intersection Theorem Collinear Formulas: Coplanar Distance Formula Segment Bisector Distance between 2 numbers Perpendicular Bisector Midpoint Formula Angle Bisector Midpoint of two numbers Supplementary Angles Constructions: Complementary Angles Perpendicular Bisector & Midpoint Linear Pair Angle Bisector Vertical Angles Congruent Segment Adjacent Angles Congruent Angles 1. Name the three undefined geometric terms. ________________ ________________ ________________ 2. True or False. In Euclidean geometry, two different lines intersect in at most one point. Explain your answer in complete sentence form. ________________________________________________________________________________________________ 3. Use the diagram provided. The lines are labeled a, b, and c. a. Name a line containing P. b. Name 3 non-coplanar points. ____________ ____ c. Name 3 collinear points. ____________ ____________ 4. S is between R and T, if RS = 7a and ST = 12a and RT = 76, find the value of a and RS. ______________ ______________ 5. Using the number line below, find ST. ______________ 6. On the segment below, M is the midpoint of XY , MY = 3x + 3, and XM = 5x – 9. a. Write an equation that will help you find x. 7. Are ______________ b. Solve for x. ______________ c. Find XY ______________ # LS and # SL the same set of points? Explain why or why not. __________________________________________________________________________ 8. Suppose that m∠AXB = 43°. a. Name a linear pair. __________________ b. Name a pair of vertical angles. __________________ c. Find m∠CXD __________________ d. Find m∠BXD __________________ 9. An angles measure is 14 times the measure of its complement. Find the measure of the angle and its complement. __________________ 10. Suppose ∠1 and ∠2 form a linear pair with m∠1 = (8j + 1)° and m∠2 = (9j + 9)° a. Find j __________________ b. Find m∠2 __________________ 11. Using the points A(5, -2) and B(-1, 6) calculate the following. a. Find the distance between A and B. b. Find the midpoint of 12. In the figure below, AB . __________________ __________________ # DB bisects ∠ADC. What is m∠ADC? __________________ Chapter 2 Topics: Conjecture Write a two column proof Deductive Reasoning Properties of Equality Inductive Reasoning Properties of Congruence 13. Find the measure of each numbered angle below if m∠4 = (2x + 1)° and m∠6 = (6x – 7). ____________ ____________ ____________ ____________ 14. Find the measure of each numbered angle below if m∠3 = (8x + 13)° and m∠4 = (14x + 2). ____________ ____________ ____________ ____________ 15. Tell whether each of the following is inductive or deductive reasoning. a. Sam notices that every morning his little brother wakes up first and runs into Sam's bedroom to wake him up. Sam goes to sleep for the night and assumes that his little brother will come in and wake him up in the morning. _________________________________________________________ b. There is a myth that the Great Wall of China is the only manmade object visible from the moon. The Great Wall is barely visible in photographs taken from 180 miles above the Earth. The moon is 237,000 miles from Earth. Therefore, the myth can't be true. _________________________________________________________ 16. What property of equality is illustrated by: If 4x + 9 = 5, then 4x = - 4. ____________________________ 17. Write a two column proof. Given: B is the midpoint of Prove: AB = CD Statements Reasons AC and C is the midpoint of BD 1. 1. 2. 2. 3. 3. 18. Solve and prove. Given: 5(x + 3) = -7x + 195 Prove: x = 15 Statements Reasons 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. 6. 6. Chapter 3 Topics: Transversals Equidistant Proving Lines Parallel Parallel Lines Distance Parallel Planes Alt. Ext. Angles Alt. Int. Angles Same side interior angles Same side exterior angles Point Slope Form Slope Intercept Form Slope Vertical Angles Corresponding Angles Constructions: Linear Pair A line through a point parallel to a given segment A line through a point perpendicular to a given segment 19. Give an equation for a line perpendicular to the line 2 y= x"5 passing through (2, 3) in point-slope form. 3 _____________________ 20. Give an equation for the line that goes through the points (1, 5) and (3, 1) in slope-intercept form. _____________________ 21. Use the figure below, where m // n. If m∠1 = 140° , then find m∠8. _____________________ 22. Using the figure above, where m // n. If m∠3 = 15x + 4 and m∠6 = 11x + 15. Find m∠6. _____________________ 23. In the figure below p // q. If m∠6 = (6g + 4)° and m∠3 = (15g + 8)°. Find m∠3. _____________________ 24. Write an equation in slope-intercept form for the line with slope -5 and y-intercept of 7. _____________________ 25. Write an equation in slope-intercept form for the line through (2, - 4) and (-1, 5). _____________________ 26. Find the value of x which makes m // n. _____________________ 27. Construct the line through point P that is parallel to the given segment. 28. Construct the line through point P that is perpendicular to the given segment. Chapter 4 Topics: Acute, Right, Obtuse Triangles Scalene, Isosceles, Equilateral Triangles Use distance formula to classify triangles Triangle Sum Theorem Exterior Angle Theorem Triangle Congruence (SSS, SAS, ASA, AAS, HL) CPCTC Reflexive Property Isosceles Triangle Theorem Equilateral Triangle Theorem 29. Name the triangle shown below which fits each description. Choose the best answer in each case. a. scalene triangle b. isosceles triangle c. equilateral triangle 30. The extended ratio of the angles in ∆EFG is 3:5:7. Find all three angle measures. 31. What triangle congruence theorem proves that the triangles below are congruent? _____________________ _____________________ _____________________ _______ ________ ________ _____________________ 32. Using the diagram at the right, give the additional piece of information that would be needed to say that the two triangles are congruent by the following theorems: a. ASA Congruence Theorem ____________________ b. SAS Congruence Theorem ____________________ c. AAS Congruence Theorem ____________________ 33. In the figure below, m∠M = 4t° and m∠P = 13t°, find m∠PNO. _____________________ 34. Classify ∆ABC based on its side lengths with A(-3, 4), B(-3, 9), C(1, 7). A graph is not sufficient evidence. You must show calculations that support your answer. _____________________ 35. Using the figure below, find m∠A and m∠B. _____________________ _____________________ 36. Complete the missing portions of the proof below. Given: M is the midpoint of RS ; ∠URM ≅ ∠TSM. Prove: ∆RMU ≅ ∆SMT Statements RS ; m∠URM ≅ m∠TSM. 1. M is the midpoint of Reasons 1. Given 2. 2. 3. 3. 4. 4. 37. If ∆ABC is an isosceles triangle with vertex ∠B, then find the value of x and m∠B when m∠A = (77- x)º, m∠B = (3x + 12)º, and m∠C = (4x + 7)º. _____________________ _____________________ 38. Complete the proof below. Given: LQ ≅ NP ; ∠NLQ ≅ ∠LNP Prove: QN ≅ PL Statements Reasons 1 1. 2. 2. 3. 3. 4. 4. Chapter 5 Topics: Perpendicular Bisector Angle Bisector Median Altitude Circumcenter Incenter Centroid Orthocenter Calculate Centroid and Circumcenter in coordinate plane Triangle Midsegment Theorem Triangle Inequality Theorem Calculate slope, midpoint, distance. Hinge Theorem Construct: Angle-Side Relationships Circumcenter, Incenter, Centroid, Median 39. List the angles of the triangle with the given vertices in order from smallest to largest. Show all of your work used in calculating the distance of each side. X(-3, -2), Y(3, 2), Z(-3, -6) 40. Find the range of measures of the third side of a triangle with side lengths 23 and 39. _____________________ 41. Is it possible to form a triangle with the given side lengths? Explain your answer. 9.9cm, 1.1cm, 8.2cm _____________________ 42. List the sides of the triangle in order from smallest to largest. _____________________ 43. State whether each statement is always, sometimes, or never true. Explain your answer. a. The medians of a triangle intersect at one of the vertices of the triangle. _____________________ b. The angle bisectors of a triangle intersect at a point in the interior of the triangle. _____________________ 44. Name the point of concurrency of the angle bisectors of a triangle. 45. In ∆RST, if point P is the midpoint of _____________________ RS , then PT is called what? 46. Name the point of concurrency of the altitudes of a triangle? _____________________ _____________________ 47. In ∆JKL, if point H is equidistant from # KJ and # KL then HK 48. Points P, Q, and R are the midpoints of JK , KL , and JL respectively. Find x. _____________________ 49. Find FH. is called what? _____________________ _____________________ 50. What is the minimum number of perpendicular bisectors needed to construct the circumcenter? _____________________ 51. In ∆ABC, CR is a median. Find AB. _____________________ 52. Construct the incenter of ∆WIN. 53. Find the coordinates of the centroid of the triangle with the following vertices. A (0, 6), B(8, 6), C(0, -8) _____________________ 54. Compare PS and PQ _____________________ 55. Find the range of values for x. _____________________ 56. Tell whether the numbers provided can be side lengths of a triangle. If so, classify by angle measure. a. 15, 18, 20 _____________________ b. 7, 8, 11 _____________________ Chapter 6 Topics: Regular Polygons Kite Convex Trapezoid Concave Trapezoid Midsegment Theorem Parallelogram Polygon Angle Sum Theorem Rectangle Polygon Exterior Angle Sum Theorem Square Refer to chapter 6 quizzes for additional review! 57a. Find the sum of the exterior angles in a 19-gon. b. Find the measure of one exterior angle of a regular 19-gon. 58a. Find the sum of the measures of the interior angles of a regular heptagon. b. Find the measure of one interior angle in a regular heptagon. _____________________ _____________________ _____________________ _____________________ 59. Draw a figure which is a convex nonagon. _____________________ 60. Draw a figure which is not a polygon. _____________________ 61. Answer the following True or False questions using the quadrilateral hierarchy: a. All trapezoids are parallelograms. T or F b. All rhombuses are parallelograms. T or F c. All rectangles are isosceles trapezoids. T or F d. All squares are kites. T or F 62. Use the figure at the right to identify: a. A diagonal. _______________ b. Two consecutive sides. ______________ c. Two nonadjacent vertices. _____________ 63. Give the most specific name for the following quadrilaterals. 63. a. b. c. d. Use the diagram below to find: a. m∠B b. m ∠GCD a. m∠B = _____________________ b. m∠GC D =__________________