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Transcript
Geometry First Semester Exam Part I: Vocabulary acute angle acute triangle adjacent angles alternate exterior angles alternate interior angles altitude angle angle bisector base angles betweeness centroid circumcenter collinear complementary compound statement concave concurrent lines conditional statement congruence transformations congruent congruent triangles conjecture conjunction consecutive interior angles construction contradiction convex coordinate proof coplanar corollary corresponding angles corresponding angles postulate counterexample cross products deductive argument deductive reasoning degree disjunction distance equiangular triangle equidistant equilateral triangle exterior exterior angle Name __________________________________hr __ Date ____/____/____ Score: flow proof formal proof if –then statement incenter included angle included side indirect proof indirect reasoning inductive reasoning informal proof interior interior angles isosceles triangle line line segment linear pair logically equivalent means median midpoint midsegment negation n-gon non-Euclidean geometry obtuse angle obtuse triangle opposite rays orthocenter paragraph proof parallel lines parallel planes perimeter perpendicular perpendicular bisector plane plane Euclidean geometry point point concurrency point-slope form polygon precision proof proof by contradiction proportion ratio rate of change regular polygon related conditionals remote interior angles right angle right triangle scale factor scalene triangle segment bisector sides similar polygons skew lines slope slope-intercept form space spherical geometry statement supplementary transversal truth table truth value two-column proof undefined terms vertex vertex angle vertical angles Choose from the terms above to complete each sentence. 1. Two lines are ____________________________ if they intersect to form a right angle. 2. Two angles are____________________________ if their measures have a sum of 90°. 3. When two rays intersect with a common endpoint a(n) ____________________________ is formed. 4. The____________________________ is the point located halfway between the endpoints of a segment. 5. ____________________________are nonadjacent angles formed by the intersection of two lines. 6. A(n) ____________________________ divides an angle into two congruent angles. 7. Two angles are____________________________ if their measures have a sum of 180°. 8. Two angles that lie in the same plane are called____________________________ if they share a common side and a common vertex. 9. A(n) ____________________________ is an angle whose measure is less than 90°. 10. Two segments are ____________________________if they have the same measure. 11. A false example is called a ____________________________. 12. A ____________________________is an educated guess based on known information. 13. ____________________________uses facts, rules, definitions, or properties to reach logical conclusions. 14. 4 and 5 are ____________________________ . 15. According to the____________________________ , line r is parallel to line t given 3 8. 16. Given r t, then ____________________________ 4 and 6 are supplementary. 17. Line p is a _____________________ since it intersects or more lines in a plane at different points. 18. When a linear equation is written in the form y = mx + b, m is the ____________________________of the line and b is the y-intercept. 19. ____________________________ are located between the lines cut by a transversal. 20. If two lines do not intersect and are everywhere equidistant, the lines are____________________________ . 21. The Perpendicular Transversal Theorem states that in plane, if a line is perpendicular to one of two parallel lines, then it is____________________________ to the other. 22. The ratio of the rise to the run of a line is called its ____________________________. 23. A triangle that is equilateral is also called a(n) ____________________________ . 24. A(n) ____________________________has at least one obtuse angle. 25. The sum of the ____________________________is equivalent to the exterior angle of a triangle. 26. The ____________________________angles of an isosceles triangle are congruent. 27. A triangle with different measures for each side is classified as a(n) ____________________________ . 28. A ____________________________organizes a series of statements in logical order written in boxes and uses arrows to indicate the order of the statements. 29. A triangle that is translated, reflected or rotated and preserves its shape, is said to be a(n) _____________ . 30. The ASA postulate involves two corresponding angles and their corresponding______________________. 31. A ____________________________uses figures in the coordinate plane and algebra to prove geometric concepts. 32. The ____________________________is formed by the congruent legs of an isosceles triangle. 33. The ____________________________of a triangle is a segment whose endpoints are a vertex of a triangle and the midpoint of the side opposite the vertex. 34. The ____________________________of a triangle is the point where the altitudes of the triangle intersect. 35. The point of concurrency of the perpendicular bisectors of a triangle is called the ____________________. 36. The____________________________ of a triangle is the intersection of the medians of the triangle. 37. ____________________________can be used to prove statements in geometry and prove theorems. 38. The _________________________ of a triangle is the intersection of the angle bisectors of the triangle. 39. The ____________________________of a triangle is a line, segment, or ray that passes through the midpoint of a side and is perpendicular to that side. 40. The____________________________ is the point where three or more lines intersect. 41. An indirect proof is a proof where you assume that the conclusion is false and then show that this assumption leads to a __________________of the hypothesis, a definition, postulate, theorem, or some other accepted fact. 42. If there are 15 girls and 9 boys in an art class, the ____________________________of girls to boys in the class is 5:3. 43. If ABC ~ DEF, AB = 10, and DE = 2.5, then the ____________________________of ABC to DEF is 4:1. 44. In LMN, P lies on LM and Q on LN. If PQ = ½MN, PQ is called a(n) ____________________________. 45. If quadrilaterals ABCD and WXYZ have corresponding angles congruent and corresponding sides proportional, they are called ____________________________. 46. The equation 3 24 is called a(n) __________________________________. x 30 47. The ___________________________ of the product of the equation 3 24 are 24x and 90. x 30 Part II: Proofs Complete each of the following. Find the measure of each angle. a = __________ b = __________ c = __________ d = __________ e = __________ f = __________ g = __________ h = __________ 2 – 5 COMPLETE FOUR OF THE FOLLOWING PROOFS. B. Given: DF AB A. Given: 2x – 7 = 14 – x Prove: x = 7 E F A B Prove: AB = DE + EF __________________________________________ C. Given: 1 & 2 are Right Angles Prove: 1 2 D 2 1 (Do not use: All right angles congruent.) __________________________________________ __________________________________________ D. Given: 1 8 Prove: a b (Do not use: Alt exterior angles Congruent form parallel lines) __________________________________________ F. Given: PQ SR , PQ SR E. Given: L is the midpoint of WE R WR ED Prove: WR ED W E L __________________________________________ D Prove: SP QR __________________________________________ G. Given: 1 2 1 Prove: a b a (Do an indirect proof) 2 b