WEEK 2

Question 1

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

Answer 1

Trigonometry

Question 2

deals with the triangles bounded by arcs of great circles.

Answer 2

Spherical Trigonometry

Question 3

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

Answer 3

plane angle

Question 4

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

Answer 4

Reference angle

Question 5

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

Answer 5

Coterminal angles

Question 6

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

Answer 6

angle of elevation

Question 7

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

Answer 7

angle of depression

Question 8

is a triangle having no
equal sides.

Answer 8

A scalene triangle

Question 9

is a triangle having at least two equal sides.

Answer 9

An isosceles triangle

Question 10

is a triangle having three equal sides.

Answer 10

An equilateral triangle

Question 11

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

Answer 11

Centroid

Question 12

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

Answer 12

Incenter

Question 13

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

Answer 13

Circumcenter

Question 14

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

Answer 14

Orthocenter

Question 15

is the center of the escribed circle.

Answer 15

Excenter

Question 16

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

Answer 16

nine-point circle

Question 17

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

Answer 17

Euler’s line

Question 18

The incenter lies on the Euler line only for

Answer 18

Isosceles triangle

Question 19

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

Answer 19

Median

Question 20

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

Answer 20

Apollonius’ theorem

Question 21

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

Answer 21

Angle Bisector

Question 22

a segment from a vertex perpendicular to the opposite side.

Answer 22

Altitude

Question 23

“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”

Answer 23

The Pythagorean Theorem

Question 24

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

Answer 24

A unit circle

Question 25

ASTC

Answer 25

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.

Question 26

is a triangle that contains no right angle.

Answer 26

Oblique triangle

Question 27

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

Answer 27

Spherical Trigonometry

Question 28

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.

Answer 28

Mollweide's Formula

Question 29

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

Answer 29

Geometry

Question 30

The Three Undefined Terms in Geometry

Answer 30

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

Question 31

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

Answer 31

Polygon

Question 32

a polygon with all interior angles less than 180°.

Answer 32

Convex

Question 33

a polygon which has interior angle greater than 180°.

Answer 33

Concave

Question 34

polygons are named according to their

Answer 34

vertices.

Question 35

Properties of Regular Polygon

Answer 35

Diagonal, Interior angle, Exterior angle, and Central angle

Question 36

is the line segment connecting two nonconsecutive vertices f a polygon

Answer 36

Diagonal

Question 37

is the angle between two consecutive sides of a polygon

Answer 37

Interior Angle

Question 38

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

Answer 38

Central Angle

Question 39

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

Answer 39

Exterior angle

Question 40

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.

Answer 40

A quadrilateral

Question 41

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

Answer 41

Parallelogram

Question 42

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

Answer 42

A trapezoid

Question 43

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

Answer 43

A rhombus

Question 44

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

Answer 44

A rectangle

Question 45

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

Answer 45

A cyclic quadrilateral

Question 46

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

Answer 46

Ptolemy’s Theorem

Question 47

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.

Answer 47

Brahmagupta’s Theorem

Question 48

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

Answer 48

Brahmagupta

Question 49

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

Answer 49

Solid

Question 50

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

Answer 50

Polyhedron

Question 51

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.

Answer 51

A regular polyhedron

Question 52

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

Answer 52

A tetrahedron

Question 53

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

Answer 53

A prism

Question 54

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

Answer 54

Oblique Prism

Question 55

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.

Answer 55

A cylinder

Question 56

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

Answer 56

Right Prism

Question 57

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

Answer 57

A pyramid

Question 58

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

Answer 58

A cone

Question 59

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

Answer 59

Sphere

Question 60

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

Answer 60

A great circle

Question 61

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

Answer 61

small circles

Question 62

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

Answer 62

Spherical distance

Question 63

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

Answer 63

Polar distance

Question 64

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

Answer 64

Spherical Zone

Question 65

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.

Answer 65

Spherical angle

Question 66

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

Answer 66

A spherical segment

Question 67

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

Answer 67

A spherical sector

Question 68

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

Answer 68

SPHERICAL POLYGON

Question 69

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

Answer 69

A spherical pyramid

Question 70

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

Answer 70

Spherical lune

Question 71

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.

Answer 71

A torus

Question 72

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.

Answer 72

A spheroid

Question 73

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

Answer 73

PARABOLOID