What are the definitions from Discovering Geometry?

Answer 1

1. An acute angle is an angle that measures less than 90°.

2. An acute triangle is a triangle with one acute angle.

3. An altitude of a triangle is a perpendicular segment from a vertex to the opposite side or to a line containing the opposite side.

4. An angle is formed by two rays that share a common endpoint provided that the two rays are non-collinear.

5. A ray is the angle bisector if it contains the vertex and divides the angle into two congruent angles.

6. An arc measure is found by measuring the central angle.

7. An arc of a circle is two points on the circle and the continuous (unbroken) part of the circle between the two points.

8. The side opposite of the vertex is the base.

9. The two angles opposite the two sides of equal length are called the base angles.

10. The midpoint bisects the segment, or divides the segment into two congruent segments.

11. The central angle is the angle with its vertex at the center of the circle, and sides passing through the endpoints of the arc.

12. The point of concurrency of the three medians is called a centroid.

13. A chord is a line segment whose endpoints lie on a circle.

14. A circle is the set of all points in a plane at a given distance (radius) from a given point (center) in the plane.

15. The point of concurrency for the perpendicular bisectors is the circumcenter.

16. The distance around a circle is called a circumference.

17. A circle is circumscribed about a polygon if and only if it passes through each vertex of the polygon.

18. Collinear means on the same line.

19. A pair of complementary angles has a sum of 90°.

20. A polygon is concave if at least one diagonal is outside the polygon.

21. A concave kite is sometimes called a dart.

22. If two or more coplanar circles share the same center, they are concentric circles.

23. When three or more lines have a point in common they are concurrent.

24. Two angles are congruent angles if and only if they have the same measures.

25. If two or more circles have the same radius, they are congruent circles.

26. Two polygons are congruent polygons if and only if they are exactly the same size and shape.

27. Two segments are congruent segments if and only if they have the same measure or length.

28. When you use inductive reasoning to make a generalization, the generalization is called a conjecture.

29. Coplanar means on the same plane.

30. Corresponding Parts of Congruent Triangles are Congruent, CPCTC.

31. A quadrilateral inscribed in a circle is called a cyclic quadrilateral.

32. A kite is sometimes called a concave dart.

33. Deductive reasoning is the process of showing that certain statements follow logically from agreed upon assumptions and proven facts, use a set of rules or facts.

34. A definition is a statement that clarifies or explains the meaning of a word or phrase.

35. A diagonal is a line segment that connects two nonconsecutive vertexes.

36. The diameter is a line segment containing the center, with the endpoints on the circle.

37. A diameter is a chord that passes through the center, a diameter is the longest chord.

38. Each point in an image is equidistant from the point corresponds to it in the original figure , because it is the same for all the points ,this is called the distance of the translation.

39. The distance from a point to a line is the length of the perpendicular segment from the point to the line.

40. The two points are called the endpoints of the arc.

41. A line segment consists of two points called the endpoints of the segment and all the points between them are collinear with the two points.

42. In an equiangular polygon all the angles have equal measures.

43. In an equilateral polygon all sides have equal lengths.

44. An equilateral triangle is a triangle with three congruent sides.

45. A flowchart is a concept map that shows all the steps in a complicated procedure in proper order.

46. To present your reasoning in flowchart form, create a flowchart proof.

47. The rule that gives the nth term for a sequence is called the function rule.

48. An image is an exact copy of the original one.

49. The point of concurrency for 3 angle bisectors is called the incenter.

50. Inductive Reasoning is the process of observing data, recognizing patterns and making generalizations about those patterns. Have lots of experiments but use the same result.

51. A circle is inscribed if and only if it touches each side of the polygon at exactly one point.

52. An inscribed angle is an angle whose vertex is on the circle and whose sides are chords of the circle.

53. An isosceles triangle that has at least two congruent sides.

54. A kite is a quadrilateral with two distinct pairs of consecutive congruent sides.

55. The length of an arc , or arc length is some fraction of the circumference of the circle.

56. Two angles are linear pairs if they share a common vertex and a common side and their non-common sides form a line.

57. The locus of points is a set of all points in a plane that satisfy some given condition or property.

58. A major arc is an arc of a circle whose endpoints are the endpoints of the diameter.

59. The measure of an angle is the smallest amount of rotation about the vertex from one way to the other, measured in degrees.

60. The measure of an arc is equal to the measure of its central angle.

61. The segment connecting the vertex of a triangle to the midpoint of its opposite side is a median.

62. The segment that connects the midpoints of two sides of a triangle is a mid-segment.

63. The segment connecting the midpoints of two sides of a triangle is the mid-segment of a triangle.

64. The segment connecting the midpoints of the two nonparallel sides of a triangle is called the mid-segment of a triangle.

65. The midpoint of a segment is the point on a segment that is the same distance from both endpoints.

66. A minor arc is the arc of a circle that is smaller than a semi-circle.

67. Non-collinear means the ray cannot lie on the same line.

68. A transformation that does not preserve the size and shape is called nonrigid transformation

69. An obtuse angle is an angle with a measure more than 90°.

70. An obtuse triangle is a triangle with one obtuse angle.

71. The point of concurrency for the three altitudes is called the orthocenter.

72. Parallel lines are lines in the same line that never intersect.

73. A parallelogram is a quadrilateral with two pairs of parallel lines.

74. A segment has many perpendiculars and many bisectors, but each segment in a plane has only one bisector that is also perpendicular to the segment. This segment is known as the perpendicular bisector.

75. Perpendicular lines are lines that intersect at 90°.

76. A polygon is a closed figure in a plane, formed by connecting line segments endpoint to endpoint with each segment intersecting exactly two others.

77. A radius is a segment from the center to a point on the edge of a circle.

78. A segment from the center to a point on the edge of the circle is called a radius.

79. A rectangle is a quadrilateral with four congruent angles.

80. A regular polygon is both equilateral and equiangular.

81. The resultant vector of these vectors is a single vector that has the same effect. Also known as a vector sum.

82. A rhombus is an equilateral parallelogram.

83. A right angle is an angle that measures 90°.

84. A right triangle is a triangle with one right angle.

85. If an image is congruent to the original figure, the process is called rigid transformation or isometrey.

86. A scalene triangle is a triangle with no congruent sides.

87. A line that intersects a circle is called a secant.

88. A segment bisector is a ray, line or segment in a plane that passes through the midpoint of a segment in a plane.

89. A semi-circle is an arc of a circle whose endpoints are the endpoints of the diameter.

90. Each line segment is called a side of the polygon.

91. The two rays are the sides of the polygon.

92. Slope is referred to as "rise over run".

93. Writing the equation of a line using the slope intercept form.

94. Space is the set of all points.

95. A square is an equiangular rhombus, equilateral rectangle, and a regular quadrilateral.

96. A tangent is a line that intersects the circle only once.

97. Tangent circles are two circles that are tangent to same line at the same point. They can be internally tangent or externally tangent.

98. Tangential velocity is a measure of the distance of an object travels along a circular path in a given amount of time.

99. By moving all the points of the geometric figure , you can create an image of the original figure, this process is called transformation.

100. Translation is the simplest type of isometry.

101. A line intersecting two or more other lines in the plane is called a transversal.

102. A trapezoid is a quadrilateral with exactly one pair of parallel sides.

103. A vector is a quantity that has both magnitude and direction.

104. Vertical angles are angles formed by two intersecting lines, they share a common vertex but do not share a common side.

105. The common endpoint of the two rays is called the vertex.

106. Each endpoint where the sides meet is called a vertex of a polygon.

107. The two sides of equal length is called the vertex angle.

These cover up to chapter 6 i think i i have all the conjectures too