Geometry Semester 1 Exam Study Guide ..., Summaries of Geometry

Download Geometry Semester 1 Exam Study Guide ... and more Summaries Geometry in PDF only on Docsity! Geometry Semester 1 Exam Study Guide Name________________________________Date______________Block________ Preparing for the Semester Exam…  Use notes, homework, checkpoints, quizzes, and tests to prepare. If you lost any of the notes, reprint them from my web page (under Class Summary). Use the flashcards located at http://quizlet.com/3887884/mrs-g-geometry-semester-1-exam-review-flash- cards/ to help review terms, definitions, and concepts. DON’T LIMIT STUDYING TO PRACTICE PROBLEMS IN THIS STUDY GUIDE. Know:  Logic o terms: inductive reasoning, deductive reasoning, conjecture, counterexample, conditional statement, hypothesis, conclusion, negation, converse, inverse, contrapositive, Law of Detachment, Law of Syllogism o Be able to form converse/inverse/contrapositive statements from a given statement o Be able to determine if statements are equivalent (have same truth value) o Review using Venn (Euler) Diagrams to deductively draw conclusions  Basics o terms: point, line, plane, collinear, coplanar, axioms, postulates, theorems, midpoint, bisector, angles (obtuse, acute, right, complementary, supplementary, vertical, linear pair) o Be able to apply midpoint and distance formulas:  Midpoint M of points (x1, y1) and (x2, y2) =          2 21 2 21 yy , xx M  Given points A(x1, y1) and B(x2, y2) are points on the coordinate plane, then the distance between A and B is: AB = 2 ) 1 y 2 (y 2 ) 1 x 2 (x  o Be able to classify angles as acute, obtuse, or right, and find angle measures for complementary, supplementary, and vertical angles.  Parallel Lines o Given a transversal crossing two lines, be able to identify angles that are interior, exterior, alternate, consecutive, corresponding, alternate interior, alternate exterior, and consecutive interior. Know which angles are congruent or supplementary if the transversal crosses two parallel lines. o Slope: be able to find the slope given a linear equation in two variables…  Be able to write equations of lines given two points, or a point and a slope  point-slope formula: y – y1 = m(x – x1)  parallel lines have the same slope but different y-intercepts  perpendicular lines have slopes whose product is -1 (negative reciprocals of each other)  Given a line, be able to write the equation of another line that is either parallel or perpendicular to the given line through a point on the new line o Know how to apply parallel/perpendicular line theorems  Triangles o Congruent triangles :  Triangles may be proven congruent if all corresponding parts (angles and sides) are congruent; or the following postulates/theorems may be used:  SSS, SAS, ASA, AAS, HL Geometry Semester 1 Exam Study Guide Page 2  Triangles may NOT be proven congruent if all we know is AAA or SSA  Corresponding parts of congruent triangles are congruent (CPCTC)  Be able to identify whether triangles are congruent or whether corresponding parts are congruent (find triangle congruence first)  Be able to supply statements or reasons given a triangle congruence proof  Be able to apply theorems/postulates associated with isosceles triangles (such as the base angles theorem) o Triangle Inequalities:  Be able to order the sides or angles of triangle by size  Be able to determine if three side lengths can form a triangle  Given two side lengths of a triangle, give a range of possible values for the third side  Be able to apply the Hinge Theorem to determine which angles or sides of a triangle are bigger or smaller than in another triangle. o Triangle Similarity:  Be able to solve proportions.  Be able to solve problems using extended ratios (e.g. finding triangle angle measures)  Be able to find geometric means: the geometric mean of a and b is given by ab  Be able to find scale factor of similar triangles, and apply to find missing sides in a similar triangles, and to find perimeters of similar triangles.  Be able to prove similarity using AA, SSS, and SAS postulates/theorems. o Right Triangles  Use the Pythagorean Theorem to find a missing side of a right triangle.  Determine if three sides make a triangle, and, if so, is the triangle right, acute, or obtuse.  Find missing sides of a triangle given a right triangle with an altitude drawn through the right angle to the other side (use geometric mean).  Find missing sides of special right triangles (45-45-90 or 30-60-90).  Be able to apply trigonometry ratios (SOH CAH TOA) and inverse trig to find missing sides or angles of triangles. Practice Questions 1) Given the statement "If it is Monday, then we have art class," write the converse, inverse and contrapositive of the statement. Assuming the initial statement is true, what are the truth values of the other statements? 2) What is the inverse of the statement "If 84 x then 2x "? a) If 2x then 84 x b) If 2x then 84 x c) If 2x then 84 x d) If 84 x then 2x Geometry Semester 1 Exam Study Guide Page 5 15) George used a decorative fencing to enclose his deck. Using the information on the diagram and assuming the top and bottom are parallel, xm is: a) 50o b) 80o c) 100o d) 130o 16) Line l intersects lines w, x, y, and z. Which two lines are parallel? a) w and x b) w and y c) x and z d) y and z 17) BA is parallel to CD if: a) 21  mm b) 43  mm c) 9021  mm d) 4321  mmmm 18) The measure of YZV is 40o and the measure of XYZ is 65o. Which of these angles must measure 40o in order for VR to be parallel toYZ ? a) YVZ b) ZVR c) ZYV d) VRX 19) What value of x will show that lines l and m are parallel? a) 42 b) 96 c) 30 d) 6 20) Angle 1 is a complement of angle 2. If 8141  xm and 682  xm , what is the value of x and of 1m ? Geometry Semester 1 Exam Study Guide Page 6 21) What is 3m ? a) 65o b) 75o c) 85o d) 90o 22) Two angles of a triangle measure 89o and 32o. Classify the triangle by its sides and angles. a) isosceles right b) scalene acute c) equilateral equiangular d) scalene obtuse 23) Which of the following equations represent a line with slope -5 and passes through point (1, -2)? a) 5x – y = 3 b) -5x + y = 3 c) 5x + y = 3 d) 5x + y = -3 24) What is the slope of the line in the graph at right? a) 3 1 b) 3 2 c) 2 d) 3 25) Write an equation of the line perpendicular to the line shown in the graph at right (same as the previous question) and that passes through the point (-4, -3) on the perpendicular line. 26) In ABC , D is the midpoint of AB and E is the midpoint of BC . If 153  xAC and 6DE , what is the value of x? 27) What is the slope of the line perpendicular to 1037  yx ? a) 3 7 b) 7 3 c) 3 7  d) 7 3  28) What is the slope of a line parallel to the line formed by connecting coordinates (-1, 5) and (7, -3)? a) 1 b) -1 c) 4 1  d) 3 4  Geometry Semester 1 Exam Study Guide Page 7 29) If CADACB  , what is the value of x and y? 30) Which two points determine a line parallel to QR ? a)  1 ,2 and  1- ,2 b)  4 ,1 and  2 ,5 c)  1- ,1 and  3- ,2 d)  1 ,1 and  1- ,2 31) The line formed by points (5, 1), (-2, 6) and the line formed by points (-3, 10) , (2,3) are… a) parallel b) perpendicular c) not parallel or perpendicular d) unable to determine whether they are parallel or perpendicular 32) Given: BDAC  , BCAD  Which could be used to prove CDBDCA  ? a) SSS b) SAS c) ASA d) AAS 33) Given: AE and BD bisect each other at C. Which could be used to prove EDCABC  ? a) SSS b) SAS c) ASA d) AAS 34) Which of the following could be the lengths of the sides of ABC ? a) AB = 12, BC = 15, AC = 2 b) AB = 9, BC = 15, AC = 4 c) AB = 150, BC = 100, AC = 50 d) AB = 10, BC = 8, AC = 12 35) In ABC ,  59Bm and  57Cm . From shortest to longest, the sides of ∆ABC are: a) AB, BC, AC b) AC, BC, AB c) AB, AC, BC d) BC, AC, AB Geometry Semester 1 Exam Study Guide Page 10 48) An image of a target is shown. To the nearest tenth, what is the value of x? 49) What is the value of x? Round to the nearest tenth. 50) Find  to the nearest tenth of a degree. 51) Given a triangle with the following sides: 7cm, 10cm, and 11 cm. Is the triangle acute, obtuse, or right? 52) In the diagram, xxAm 62  , 32  xBm , and 279  xACDm . What is Am ? 53) Given: AD bisects BC at E BCAB  BCDC  Prove: DCAB  Statements Reasons 1) AD bisects BC at E 1)_______________________ 2) ___________________ 2) Def. of segment bisector 3) BCAB  3)_______________________ 4) ABC is a rt angle 4)_______________________ 5) BCDC  5)_______________________ 6) DCE is a rt angle 6)_______________________ 7) ___________________ 7) All rt. angles are  8) DECAEB  8)_______________________ 9) DECAEB  9)_______________________ 10) DCAB  10)_______________________ Geometry Semester 1 Exam Study Guide Page 11 Answers: 1) conv: If we have art class then it is Monday. (F) Inv: If it is not Monday, then we don't have art class. (F) contra: If we don't have art class, then it isn't Monday (T) 2) d 3) d 4) a, d 5) d 6) a, b 7) a, c 8) c 9) d 10) d 11) a 12) b 13) a 14) a, b, c 15) a 16) c 17) d 18) b 19) c 20) x = 4,  641m 21) c 22) b 23) c 24) a 25) y=-3x-15 26) x=9 27) d 28) b 29) x=8, y=12 30) d 31) c 32) a 33) b 34) d 35) d 36) c 37) c 38) a, c 39) c 40) d 41) c 42) BD=6, AB= 53 43) x = 2100 y = 350 z = 100 P = 500 44) a = 12 d = 7.2 e = 12.8 f = 9.6 45) 50o 46) a 47) 28.3 ft 48) 13.2 in. 49) 21.2 50) 56.3o 51) acute 52) 135o 53) 1) given 2) CEBE  3) given 4) def. of perpendicular 5) given 6) def. of perpendicular 7) DCEABC  8) vertical angles are  9) ASA 10) CPCTC