Geometry Mid-Term Exam Review Unit #1 Unit #6 ( )

Transcription

1 Geometry Mid-Term Exam Review Unit #1 Unit #6 ( ) Chapter 1 Topics: Unique Line Assumption Flat Plane Assumption Line Intersection Theorem Collinear Coplanar Segment Bisector Perpendicular Bisector Angle Bisector Supplementary Angles Complementary Angles Linear Pair Vertical Angles Adjacent Angles Name: Due Angle Addition Postulate Segment Addition Postulate Formulas: Distance Formula Distance between 2 numbers Midpoint Formula Midpoint of two numbers Constructions: Perpendicular Bisector & Midpoint Angle Bisector Congruent Segment 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.

2 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. b. Solve for x. c. Find XY 7. Are #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 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 AB. 12. In the figure below, #DB bisects ADC. What is m ADC?

3 Chapter 2 Topics: Conjecture Deductive Reasoning Inductive Reasoning Write a two column proof Properties of Equality 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 = Write a two column proof. Given: B is the midpoint of AC and C is the midpoint of BD Prove: AB = CD Statements Reasons

4 18. Solve and prove. Given: 5(x + 3) = -7x Prove: x = 15 Statements Reasons Chapter 3 Topics: Transversals Proving Lines Parallel Distance Alt. Ext. Angles Same side interior angles Point Slope Form Slope Corresponding Angles Linear Pair Equidistant Parallel Lines Parallel Planes Alt. Int. Angles Same side exterior angles Slope Intercept Form Vertical Angles Constructions: 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 y= 2 x"5 passing through (2, 3) in point-slope form 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 Using the figure above, where m // n. If m 3 = 15x + 4 and m 6 = 11x Find m 6.

5 23. In the figure below p // q. If m 6 = (6g + 4) and m 3 = (15g + 8). Find m Write an equation in slope-intercept form for the line with slope -5 and y-intercept of 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 Use distance formula to classify triangles Exterior Angle Theorem CPCTC Isosceles Triangle Theorem Scalene, Isosceles, Equilateral Triangles Triangle Sum Theorem Triangle Congruence (SSS, SAS, ASA, AAS, HL) Reflexive Property Equilateral Triangle Theorem

6 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.

7 36. Complete the missing portions of the proof below. Given: M is the midpoint of RS ; URM TSM. Prove: RMU SMT Statements 1. M is the midpoint of RS ; m URM m TSM. 1. Given Reasons 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 1 1. Reasons Chapter 5 Topics: Perpendicular Bisector Median Circumcenter Centroid Calculate Centroid and Circumcenter in coordinate plane Triangle Inequality Theorem Hinge Theorem Angle-Side Relationships Angle Bisector Altitude Incenter Orthocenter Triangle Midsegment Theorem Calculate slope, midpoint, distance. Construct: Circumcenter, Incenter, Centroid, Median

8 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 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 is called what? 48. Points P, Q, and R are the midpoints of JK, KL, and JL respectively. Find x. 49. Find FH.

9 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

10 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 Convex Concave Parallelogram Rectangle Square Kite Trapezoid Trapezoid Midsegment Theorem Polygon Angle Sum Theorem Polygon Exterior Angle Sum Theorem 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.

11 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. a. b. c. d. 63. Use the diagram below to find: a. m B = a. m B b. m GCD b. m GC D =