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ALGEBRA > WEEK 2 > Flashcards

WEEK 2 Flashcards

1
Q

is a branch of mathematics that studies triangles and the relationships between their sides and the angles between sides.

A

Trigonometry

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2
Q

deals with the triangles bounded by arcs of great circles.

A

Spherical Trigonometry

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3
Q

determined by rotating a ray (half-line) about its endpoint called vertex.

A

plane angle

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4
Q

for an angle in standard position is the positive acute angle between the x-axis and the terminal side of angle .

A

Reference angle

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5
Q

Two angles which when placed in standard position, have coincident terminal sides

A

Coterminal angles

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6
Q

is the angle from the horizontal up to the line of sight from the observer to an object above.

A

angle of elevation

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7
Q

it is the angle from the horizontal down to the line of sight from the observer to an object below.

A

angle of depression

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8
Q

is a triangle having no
equal sides.

A

A scalene triangle

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9
Q

is a triangle having at least two equal sides.

A

An isosceles triangle

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10
Q

is a triangle having three equal sides.

A

An equilateral triangle

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11
Q

is the point of intersection of all the medians of a triangle.

A

Centroid

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12
Q
  • is the point of intersection of all angle bisectors in a triangle.
  • is also the center of the inscribed circle in a triangle.
A

Incenter

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13
Q
  • is the point of intersection of all perpendicular bisectors of a triangle.
  • is also the center of the circumscribed circle.
A

Circumcenter

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14
Q

is the point of intersection of all the altitudes of a triangle.

A

Orthocenter

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15
Q

is the center of the escribed circle.

A

Excenter

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16
Q

is a circle that can be constructed for any given triangle by passing through nine significant points defined from the
triangle.

A

nine-point circle

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17
Q

A line that passes through centroid, circumcenter, orthocenter, and the center of a nine-point circle of a triangle is called

A

Euler’s line

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18
Q

The incenter lies on the Euler line only for

A

Isosceles triangle

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19
Q

a triangle is a segment from vertex to the midpoint of the opposite side.

A

Median

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20
Q

It is a theorem relating the length of a median of a triangle to the lengths of its sides. Specifically, in any triangle ABC, if “m” is a median

A

Apollonius’ theorem

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21
Q

is a segment or ray that bisects an angle and extends to the opposite side.

A

Angle Bisector

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22
Q

a segment from a vertex perpendicular to the opposite side.

A

Altitude

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23
Q

“In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs”

A

The Pythagorean Theorem

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24
Q

is a circle on the Cartesian Plane that has a radius of 1 unit and is centered at the origin (0, 0).

A

A unit circle

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25
Q

ASTC

A

Add : All functions in the first quadrant are positive.
Sugar : Sine is positive in the second quadrant.
To : Tangent is positive in the third quadrant.
Coffee : Cosine is positive in the fourth quadrant.

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26
Q

is a triangle that contains
no right angle.

A

Oblique triangle

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27
Q

is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are great circles

A

Spherical Trigonometry

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28
Q

sometimes referred to in older texts as Mollweide’s equations, named after Karl Mollweide, is a set of two relationships between sides and angles in a triangle. It can be used to check solutions of triangles.

A

Mollweide’s Formula

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29
Q

is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

A

Geometry

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30
Q

The Three Undefined Terms in Geometry

A
  1. Point
  2. Line
  3. Plane – a flat surface without thickness
31
Q

It is a closed plane figure bounded by straight line segments as sides and with 3 or more angles.

A

Polygon

32
Q

a polygon with all interior angles less than 180°.

A

Convex

33
Q

a polygon which has interior angle greater than 180°.

A

Concave

34
Q

polygons are named according to their

A

vertices.

35
Q

Properties of Regular Polygon

A

Diagonal, Interior angle, Exterior angle, and Central angle

36
Q

is the line segment connecting two nonconsecutive vertices f a polygon

A

Diagonal

37
Q

is the angle between two consecutive sides of a polygon

A

Interior Angle

38
Q

is the angle subtended by any side and the center of the polygon.

A

Central Angle

39
Q

is the angle formed by the extension of any side of a polygon and the next adjacent side.

A

Exterior angle

40
Q

is defined as a two dimensional shape with four sides, four vertices and four angles. The various subcategories of convex quadrilaterals are trapezoid, parallelogram, rectangle, rhombus and square.

A

A quadrilateral

41
Q

is a quadrilateral in which opposite sides are parallel and equal.

A

Parallelogram

42
Q

is a quadrilateral with only one pair of opposite sides parallel.

A

A trapezoid

43
Q

is a quadrilateral in which all sides are equal but none of the angles is 90°.

A

A rhombus

44
Q

is a quadrilateral in which pairs of opposite sides are parallel and equal and each angle is 90°.

A

A rectangle

45
Q

is a quadrilateral in which all of its four vertices lie on a circle

A

A cyclic quadrilateral

46
Q

For a cyclic quadrilateral, the sum of the products of the two pairs of opposite sides equals the product of the diagonals

A

Ptolemy’s Theorem

47
Q

states that if a cyclic quadrilateral is orthodiagonal (that is, has perpendicular diagonals), then the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side.

A

Brahmagupta’s Theorem

48
Q

a Hindu mathematician of the seventh century AD who discovered a neat formula for the area of a cyclic quadrilateral.

A

Brahmagupta

49
Q

any limited portion of space bounded by surfaces or plane figures.

A

Solid

50
Q

is a solid bounded by flat surfaces with each surface bounded by straight sides.

A

Polyhedron

51
Q

is a solid figure each of whose sides is a regular polygon (of the same size) and each of whose angles is formed by the same number of sides.

A

A regular polyhedron

52
Q

is a polyhedron composed of four triangular faces, three of which meet at each vertex.

A

A tetrahedron

53
Q

is a polyhedron having two identical and parallel faces (usually referred to as the “ends” or “bases” ) and whose sides are parallelogram

A

A prism

54
Q

A prism with an axis that is not at right angle
to the base.

A

Oblique Prism

55
Q

is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given line segment, the axis of the cylinder.

A

A cylinder

56
Q

A prism is one whose axis is perpendicular to the base.

A

Right Prism

57
Q

is a polyhedron having any polygons as one face (base) with all other faces (sides) being triangles meeting at a common vertex.

A

A pyramid

58
Q

is a tree dimensional shape formed by a straight line when one end is moved around a simple closed curve, while the other end of the line is kept fixed at a point which is not in the plane of the curve

A

A cone

59
Q

is a three-dimensional surface, all points of which are equidistant from a fixed point

A

Sphere

60
Q

is a section of a sphere that contains a diameter of the sphere .

A

A great circle

61
Q

Sections of the sphere that do not contain a diameter are called

A

small circles

62
Q

the length of the minor arc of a great circle joining them and this distance is the shortest on the sphere.

A

Spherical distance

63
Q

is the spherical distance from any point on the circle to its nearest pole.

A

Polar distance

64
Q

It is a surface of revolution of a sphere
included between two parallel planes.

A

Spherical Zone

65
Q

is the angle formed by two intersecting arcs of great circles and this angle is equal to the angle formed by two lines which are tangent to the arcs at their point of intersection.

A

Spherical angle

66
Q

is the solid formed by passing two parallel cutting planes through a sphere.

A

A spherical segment

67
Q

is the solid generated by revolving a sector of a semicircle about its diameter as an axis.

A

A spherical sector

68
Q

A closed geometric figure on the surface of a sphere formed by the arcs of great circles.

A

SPHERICAL POLYGON

69
Q

is a solid whose base is a spherical polygon and whose vertex is the center of the sphere.

A

A spherical pyramid

70
Q

is an area on a sphere bounded by two half great circles, which is also called a digon or a diangle or (in German) a Zweieck

A

Spherical lune

71
Q

is a solid formed generated by rotating a circle about an axis that is in the plane of the circle but not intersecting the circle.

A

A torus

72
Q

is a kind of ellipsoid generated when an ellipse is revolved around one of its axes, given that two axes of the ellipsoid are equal.

A

A spheroid

73
Q

A solid formed by rotating a parabolic segment about axis of symmetry.

A

PARABOLOID

ALGEBRA (2 decks)

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