Analytic Geometry Vocabulary Cards and Word Walls Important Notes for Teachers:

Transcription

1 Analytic Geometry Vocabulary Cards and Word Walls Important Notes for Teachers: The vocabulary cards in this file reflect the vocabulary students taking Coordinate Algebra will need to know and be able to use. The cards are arranged alphabetically. Each card has three sections. o Section 1 is only the word. This is to be used as a visual aid in spelling and pronunciation. It is also used when students are writing their own kid-friendly definition and drawing their own graphic. o Section 2 has the word and a graphic. This graphic is available to be used as a model by the teacher. o Section 3 has the word, a graphic, and a definition. This section can be used for the Word Wall in the classroom. These cards are designed to help all students with math content vocabulary, including ELL, Gifted and Talented, Special Education, and Regular Education students.

2 major arc major arc major arc Given two points on a circle, the major arc is the longest arc connecting the two points.

3 median (of a triangle) median (of a triangle) median (of a triangle) The segment joining one vertex of a triangle to the midpoint of the side opposite the vertex

4 midsegment midsegment midsegment. The segment joining the midpoints of two sides of a triangle

5 minor arc minor arc minor arc Given two points on a circle, the minor arc is the shortest arc linking them.

6 monomial expression monomial expression monomial expression An algebraic expression with one term

7 Multiplication Rule Multiplication Rule Are the events independent? Multiplication Rule Are the events independent? If events A and B are independent, then the probability of A and B can be found by multiplying the probabilities together: ( ) ( ) ( )

8 mutually exclusive events mutually exclusive events mutually exclusive events Two events that cannot occur simultaneously, meaning that the probability of the intersection of the two events is zero; also known as disjoint events.

9 n th roots n th roots n th roots The number that must be multiplied by itself n times to equal a given value

10 opposite side opposite side opposite side In reference to an angle of a triangle, the opposite side is the side of the triangle that does not form the angle.

11 orthocenter orthocenter orthocenter The point of concurrency of the altitudes of a triangle

12 outcome outcome outcome A possible result of an experiment

13 overlapping events overlapping events overlapping events Events that can occur simultaneously they have an intersection

14 parabola parabola parabola The set of all points in a plane equidistant from a fixed line, called the directrix, and a fixed point, called the focus

15 parallel lines parallel lines parallel lines Two lines are parallel if they lie in the same plane and they do not intersect.

16 perfect square trinomial perfect square trinomial perfect square trinomial A trinomial that factors into two identical binomial factors

17 perpendicular bisector perpendicular bisector perpendicular bisector A perpendicular line or segment that passes through the midpoint of a segment

18 perpendicular lines perpendicular lines perpendicular lines Two lines are perpendicular if they intersect at a right angle.

19 plane plane Three planes intersecting plane Three planes intersecting One of the basic undefined terms of geometry Traditionally thought of as going on forever in all directions (in twodimensions) and is flat (i.e., it has no thickness).

20 point point point 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.

21 point of tangency point of tangency point of tangency The point where a tangent line touches a circle

22 polynomial function polynomial function polynomial function A polynomial function has terms that only have positive integer exponents combined by addition and/or subtraction

23 properties of equality properties of equality properties of equality Properties of equality allow an equation to be transformed while maintaining the equality of the quantities on each side of the equation symbol; properties of equality can also be used to make logical arguments

24 proportion proportion proportion An equation which states that two ratios are equal

25 Pythagorean Theorem Pythagorean Theorem Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs.

26 quadratic equation quadratic equation quadratic equation An equation of degree 2, which has at most two solutions

27 quadratic function quadratic function quadratic function A function of degree 2 which has a graph shaped like a U (can be right-side up or upside down)

28 radius radius radius The distance from the center of a circle to any point on the circle. Also, the line segment that has the center of the circle as one endpoint and a point on the circle as the other endpoint.

29 ratio ratio ratio Comparison of two quantities by division and may be written as r/s, r:s, or r to s

30 rational exponents rational exponents rational exponents For a > 0, and integers m and n, with n > 0, m a n n a m n a m ; a m/n = (a 1/n ) m = (a m ) 1/n

31 rational expression rational expression rational expression A quotient of two polynomials with a nonzero denominator

32 rational number rational number rational number A number expressible in the form a/b or a/b for some fraction a/b. The rational numbers include the integers.

33 ray ray ray A ray begins at a point and goes on forever in one direction

34 reflection reflection reflection A transformation that "flips" a figure over a line of reflection

35 reflection line reflection line 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.

36 regular polygon regular polygon regular polygon A polygon that is both equilateral and equiangular

37 remote interior angles (of a triangle) remote interior angles (of a triangle) remote interior angles (of a triangle) The two angles nonadjacent to the exterior angle

38 root root root The x-values where the function has a value of zero

39 rotation rotation rotation A transformation that turns a figure about a fixed point through a given angle in a given direction.

40 same-side exterior angles same-side exterior angles same-side exterior angles Pairs of angles formed when a third line (a transversal) crosses two other lines. These angles are on the same side of the transversal and are outside the other two lines. When the two other lines are parallel, same-side exterior angles are supplementary.

41 same-side interior angles same-side interior angles same-side interior angles Pairs of angles formed when a third line (a transversal) crosses two other lines. These angles are on the same side of the transversal and are between the other two lines. When the two other lines are parallel, same-side interior angles are supplementary.

42 sample space sample space sample space The set of all possible outcomes from an experiment

43 scale factor scale factor scale factor Scale factor of Dad s cup to Mom s cup: 3:2 The ratio of any two corresponding lengths of the sides of two similar figures

44 secant line secant line secant line A line in the plane of a circle that intersects a circle at exactly two points

45 secant segment secant segment secant segment is a secant segment A segment that contains a chord of a circle and has exactly one endpoint outside of the circle is a secant segment

46 sector sector sector The region bounded by two radii of the circle and their intercepted arc

47 set set set A collection of numbers, geometric figures, letters, or other objects that have some characteristic in common

48 similar figures similar figures similar figures Figures that have the same shape but not necessarily the same size

49 similar triangles similar triangles similar triangles Triangles are similar if they have the same shape but not necessarily the same size. Triangles whose corresponding angles are congruent are similar. Corresponding sides of similar triangles are all in the same proportion.

50 skew lines skew lines skew lines Two lines that do not lie in the same plane (therefore, they cannot be parallel or intersect).

51 slant height slant height slant height The diagonal distance from the apex of a right circular cone or a right regular pyramid to the base

52 standard form standard form standard form Polynomial: Written so that the terms are in decreasing powers of the variable Circle: Written so that the center, (h,k), and radius, r, are easily seen in the equation: ( ) ( )

53 subset subset Olive oil is a subset of cooking oils. subset A set in which every element is also contained in a larger set Olive oil is a subset of cooking oils

54 supplementary angles supplementary angles supplementary angles Two angles whose sum is 180 degrees.

55 tangent line tangent line tangent line A line in the plane of a circle that intersects a circle at only one point, the point of tangency

56 transformation transformation transformatio n The mapping, or movement, of all the points of a figure in a plane according to a common operation

57 translation translation translation A transformation that "slides" each point of a figure the same distance in the same direction

58 transversal transversal transversal A line that crosses two or more lines

59 trinomial trinomial trinomial An algebraic expression with three unlike terms

60 union of sets union of sets union of sets The set of all elements that belong to at least one of the given two or more sets denoted by

61 Venn diagram Venn diagram Venn diagram A picture that illustrates the relationship between two or more sets

62 vertex vertex vertex The maximum or minimum value of a parabola, either in terms of y if the parabola is opening up or down, or in terms of x if the parabola is opening left or right

63 vertex form vertex form vertex form A formula for a quadratic equation of the form f (x) = a (x h) 2 + k, where a is a nonzero constant and the vertex of the graph is the point (h, k)

64 vertical angles vertical angles vertical angles Two nonadjacent angles formed by intersecting lines or segments

65 whole numbers whole numbers whole numbers The numbers 0, 1, 2, 3,