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Geometry Name __________________________________hr __ First Semester Exam REVIEW Part I: Vocabulary Date ____/____/____ Score: Some terms may be used more than once. ratio acute angle flow proof rate of change acute triangle formal proof regular polygon adjacent angles if –then statement related conditionals alternate exterior angles incenter remote interior angles alternate interior angles included angle right angle altitude included side right triangle angle indirect proof scale factor angle bisector indirect reasoning scalene triangle base angles inductive reasoning segment bisector betweeness informal proof sides centroid interior similar polygons circumcenter interior angles skew lines collinear isosceles triangle slope complementary line slope-intercept form compound statement line segment space concave linear pair spherical geometry concurrent lines logically equivalent statement conditional statement means supplementary congruence transformations median transversal congruent midpoint truth table congruent triangles midsegment truth value conjecture negation two-column proof conjunction n-gon undefined terms consecutive interior angles non-Euclidean geometry vertex construction obtuse angle vertex angle contradiction obtuse triangle vertical angles convex opposite rays coordinate proof orthocenter coplanar paragraph proof corollary parallel lines corresponding angles parallel planes corresponding angles postulate perimeter counterexample perpendicular cross products perpendicular bisector deductive argument plane deductive reasoning plane Euclidean geometry degree point disjunction point concurrency distance point-slope form equiangular triangle polygon equidistant precision equilateral triangle proof exterior proof by contradiction exterior angle proportion 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(n) ____________________________ 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 two 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(n) ____________________________ 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(n) ____________________________ 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 = __________