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Mathematics: Formulas & Terms > 5. Geometry: Terms > Flashcards

5. Geometry: Terms Flashcards

1
Q

Acute Angle

A
  1. An angle which measures strictly between 0 degrees and 90 degrees is acute
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2
Q

Acute Triangle

A
  1. A triangle with each of its three interior angles acute
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3
Q

Alternate Interior Angles

A
  1. Given a pair of lines and a transversal, a pair of nonadjacent angles sitting between the pair of lines and positioned on opposite sides of a transversal are alternate interior angles (Alternate interior angles are congruent precisely when the two lines are parallel)
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4
Q

Angle Bisector

A
  1. A line that divides a given angle into two congruent angles is an angle bisector for that angle
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5
Q

Arc

A
  1. For two given points on a circle, a section of the circumference of the circle between them is called an arc of the circle. The measure of an arc is the measure of the angle between the two radii connecting those two given points. (There are two choices of angle between the two radii. The region between the two radii that contains the given are defines which angle to measure.)
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6
Q

Arc Length

A
  1. The length of an arc of a circle
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7
Q

Bisects

A

A point M sitting on a line segment AB is said to bisect the line segment if AM = MB

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8
Q

Central Angle

A
  1. An angle formed by two radii of a circle (This also defines the measure of the arc contained in the region specified by the angle)
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9
Q

Chord

A
  1. A line segment connecting two points on a circle
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10
Q

Circumcenter of a Triangle

A
  1. The center of the circumcircle of a triangle is its circumcenter. It is the location where the three perpendicular bisectors of the triangle coincide
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11
Q

Circumcircle of a Triangle

A
  1. For each triangle, there is a unique circle that passes through the vertices of the triangle. This circle is the circumcircle for the triangle
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12
Q

Collinear

A
  1. Two or more points are collinear if they lie on a common line
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13
Q

Complex Number

A
  1. A number of the form a + ib, with a and b each a real number and i an alleged quantity with the mathematical property that i^2 = -1
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14
Q

Concave Polygon

A
  1. A polygon that in not convex
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15
Q

Cone

A
  1. A figure in three-dimensional space formed by (a) drawing a region in a plane (This will be called the base of the cone) (b) selecting a point (P) anywhere above or below the plane (This will be called the cone point) (c) drawing a line segment from each and every point on the boundary of the planar region to the chosen point P
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16
Q

Congruent Angles

A
  1. Two angles of the same measure are congruent
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17
Q

Congruent Line Segments

A
  1. Two line segments of the same length are congruent
18
Q

Congruent Polygons

A
  1. Two polygons that are similar with scale factor k = 1 are congruent
19
Q

Constructible Number

A
  1. A real number a is said to be constructible if, using only a straightedge (a ruler with no makings) and a compass as tools, it is possible to draw a line segment of length a if given only a line segment of length 1 already drawn on the page
20
Q

Convex Polygon

A
  1. A polygon with the property that for any two points A and B in the interior of the polygon, the line segment AB also wholly lies in the interior of the polygon
21
Q

Coplanar

A
  1. Two or more points are coplanar if they lie on a common plane
22
Q

Cosine of an Angle (in circle-ometry)

A
  1. A point moves in a counterclockwise direction along a circle of radius 1. If the angle of elevation of the point above the positive horizontal axis is x, then the length of the horizontal displacement, left or right, of the point is denoted cos(x) and is called the cosine of the angle. (The cosine of an angle is deemed negative if the point is displaced to the left)
23
Q

Cosine of an Angle (In Trigonometry)

A
  1. If x is a non-right angle in a right triangle, then the ratio of the length of the side of the triangle adjacent to the angle x (different from the hypotenuse) to the length of the hypotenuse of the right triangle is called the cosine of the angle and is denoted cos(x). (This value matches the “over-ness” of a point on a unit circle with angle of elevation x)
24
Q

Corresponding Angles

A
  1. For a transversal crossing a pair of lines, two angles on the same side of the transversal, with one between the pair of lines and one not, are corresponding angles (Corresponding angles are congruent precisely when the two lines are parallel)
25
Q

Cylinder

A
  1. A figure in three-dimensional space formed by connecting, with straight line segments, matching boundary points of two congruent two-dimensional figures lying in parallel planes. The two planar figures (called the bases of the cylinder) are oriented so that any two connecting line segments are parallel. If the line segments connecting matching boundary points are perpendicular to the planes containing the bases, then the cylinder is a right cylinder. Otherwise, the cylinder is oblique
26
Q

Deductive Reasoning

A
  1. The process of establishing the validity of a result by logical reasoning
27
Q

Diameter

A
  1. A chord of a circle that passes through the center of the circle is called a diameter of the circle. The length of any such diameter is called a diameter of the circle. (And as lengths, the diameter of a circle is twice the radius of the circle)
28
Q

Dilation

A
  1. A dilation in the plane from a point O with scale factor k is the mapping that takes each point P different from O to a point P’ on the ray OP such that OP’ = kOP. The dilation keeps the point O itself fixed in place
29
Q

Ellipse

A
  1. Given two points F and G in the plane, the set of all points P for which the sum of distances FP + PG has the same constant value traces a curve called an ellipse. The points F and G are called the foci of the ellipse
30
Q

Equiangular Polygon

A
  1. A polygon with interior angles all of the same measure
31
Q

Equidistant

A
  1. A point is said to be equidistant from two or more objects if its distance from each of those objects is the same
32
Q

Equilateral Polygon

A
  1. A polygon with all edges the same length
33
Q

Exterior Angle of a Polygon

A
  1. In extending one edge of a polygon, the angle formed by that extension and the next side of the polygon
34
Q

Fractal

A
  1. A geometric figure with the property that it can be divided into a finite number of congruent parts, each a scaled copy of the original figure
35
Q

Fractal Dimension

A
  1. If a fractal is composed of N parts, each a scaled copy of the original fractal with scale factor k, then its fractal dimesion is the number d so that k^d = 1/N
36
Q

Geometry

A
  1. The branch of mathematics concerned with the properties of space and figures, lines, curves, points, and shapes drawn in space
37
Q

Glide Reflection

A
  1. A glide reflection along a line L in a plane is the mapping that results from performing a translation in a direction parallel to L followed by a reflection about L
38
Q

Hyperbola

A
  1. Given two points F and G in the plane, the set of all points P for which the differences of distances FP - PG and GP - PF have the same constant value traces a curve called a hyperbola. The points F and G are called the foci of the hyperbola
39
Q

Hypotenuse

A
  1. The side opposite the right angle in a right triangle
40
Q

Incenter of a Triangle

A
  1. The center of the incircle of a triangle is its incenter. It is the location where the three angle bisecors of the triangle coincide
41
Q

Incircle of a Triangle

A
  1. For each triangle, there is a unique circle sitting inside the triangle tangent to each of its three sides. This circle is the incircle of the triangle

Mathematics: Formulas & Terms (6 decks)

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