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Transcript
Geometry Vocabulary Vocabulary Term 1. Point 2. Line 3. Ray 4. Line Segment Example Definition/Description One of the basic undefined terms of geometry. Traditionally thought of as having no length, width, or thickness, and often a dot is used to represent it. We usually represent a point with a dot on paper, but the dot we make has some dimension, while a true point has no dimension. One of the basic undefined terms of geometry. Traditionally thought of as a set of points that has no thickness but its length goes on forever in two opposite directions. AB denotes a line that passes through point A and B. Has no beginning or end. Cannot measure its length. A ray begins at a point and goes on forever in one direction. Must name stating the endpoint first. The part of a line between two points on the line. AB denotes a line segment between the points A and B. Can be measured. 5. Collinear Points that are on the same line are collinear 6. Plane One of the basic undefined terms of geometry. Traditionally thought of as going on forever in all directions (in two-dimensions) and is flat (i.e., it has no thickness). 7. Coplanar Points that lie on the same plane are coplanar 8. Space A boundless, three-dimensional set of all points. Contains lines and planes. 1 9. Congruent Having the same size, shape and measure. Two figures are congruent if all of their corresponding measures are equal. 10. Midpoint Divides a segment into two equal parts. 11. Bisector A bisector divides a segment or angle into two equal parts. 12. Degree 1/360 of a turn around a circle 13. Angle Angles are created by two distinct rays that share a common endpoint (also known as a vertex). ABC or B denote angles with vertex B. Naming Angles: 14. Interior/ Exterior angles An angle inside (interior) or outside (exterior) of a figure/shape. 15. Remote Interior angles of a Triangle The two angles non-adjacent to the exterior angle. 16. Right angle An angle whose measure is exactly 90 degrees. 2 17. Acute angle An angle whose measure is between 0 and 90 degrees. 18. Obtuse angle An angle whose measure is greater than 90 but less than 180 degrees. 19. Opposite Rays/ Straight Angle Rays that share a common endpoint and extend infinitely in opposite directions. 20. Adjacent angles Angles in the same plane that have a common vertex and a common side, but no common interior points. 21. Vertical angles Two nonadjacent angles formed by two intersecting lines or segments. Also called opposite angles. 22. Linear pair A pair of adjacent angles with noncommon sides that are opposite rays. 23. Complementary angles Two angles with measures that have a sum of 90 degrees. 24. Supplementary angles Two angles with measures that have a sum of 180 degrees. 25. Perpendicular Lines, segments, or rays that intersect to form right angles. 3 26. Parallel Lines, segments, or rays that lie in the same plane but never intersect. 27. Skew Lines Two lines that do not lie in the same plane (therefore, they cannot be parallel or intersect). 28. Angles formed by parallel lines being cut by a transversal The angles have special names identifying their positions with respect to the parallel lines and transversal. They are corresponding angles, alternate exterior angles, alternate interior angles, same side interior angles, or same side exterior angles. An angle is congruent to its matched angle. 4 Same side interior: angles 3 & 6 and angles 4 & 5 Same side exterior: angles 1 & 8 and angles 2 & 7 29. Polygon A closed figure whose sides are all segments. 30. Regular polygon A convex polygon in which all the sides are congruent (equilateral) and all the angles are congruent (equiangular). 31. Similar Figures Figures that have the same shape but not necessarily the same size. 32. Correspon-ding Sides Sides that have the same relative positions in geometric figures. 33. Correspon-ding Angles Angles that have the same relative positions in geometric figures. 5 34. Transforma-tion The mapping, or movement, of all the points of a figure in a plane according to a common operation. 35. Translation A transformation that "slides" each point of a figure the same distance in the same direction 36. Dilation Transformation that changes the size of a figure, but not the shape. 37. Scale Factor The ratio of any two corresponding lengths of the sides of two similar figures. 38. Reflection A transformation that "flips" a figure over a line of reflection. 6 39. Reflection Line A line that is the perpendicular bisector of the segment with endpoints at a pre-image point and the image of that point after a reflection. 40. Rotation A transformation that turns a figure about a fixed point through a given angle and a given direction. 41. Perimeter The sum of the length of the sides of a polygon. 42. Circumference The distance around a circle. 43. Area The number of square units needed to cover a surface. The amount of space a figure takes up. 7 44. Surface area The sum of the areas of each face of a solid. 45. Volume The measure of the amount of space the solid encloses. 46. Altitude A line drawn from the vertex of a triangle perpendicular of the opposite side. 47. Median 48. Perpendicular Bisector Every triangle has 3 altitudes – one drawn from each vertex. A line drawn from the vertex of a triangle to the midpoint of the opposite side. Every triangle has 3 medians – one drawn from each vertex. A perpendicular line that passes through the midpoint of each side of a triangle. Every triangle has 3 perpendicular bisectors – one drawn through each side. 49. Angle Bisector Line drawn from the vertex of a triangle so that it bisects the angle from which it is drawn. Every triangle has 3 angle bisectors – one drawn from each vertex. 8 50. Centroid The point of concurrency of the medians of a triangle. 51. Circumcenter The point of concurrency of the perpendicular bisectors of the sides of a triangle. 52. Incenter The point of concurrency of the bisectors of the angles of a triangle. 53. Orthocenter The point of concurrency of the altitudes of a triangle. 54. Conditional Statement A statement written in if-then form. 55. Hypothesis The “if” portion of a conditional statement. 56. Conclusion The “then” portion of a conditional statement. 57. Converse The reverse of a conditional statement (reverse the hypothesis and the conclusion). 9 58. 59. 60. 61. 62. 63. 64. 65. 10