Unit 4

Further Geometry

Chapter 10,11 & 13

Geometry
= the branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogs.


SURFACE AREA
The total area of the surface of a three-dimensional object.

CUBE 

: 6 a ²

 (a is the length of the side of each edge of the cube) 

RECTANGLE

: 2ab + 2bc + 2ac

 (a, b, and c are the lengths of the 3 sides)

PRISM

: Lateral area + Area of two ends

: (perimeter of shape b) * L+ 2*(Area of shape b)

  (b is the shape of the ends)

SPHERE

: 4 pi r ²

 (r is radius of circle)

CYLINDER

:  2 pi r ² + 2 pi r h

 (h is the height of the cylinder, r is the radius of the top)

SIMILARITY

• Two figures are similar when one figure can be enlarged and superimposed so they exactly coincide
• They have the same shape, but different  size

CIRCLE GEOMETRY
It is the set of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant.

Points

Ø The basic geometric figure is a point.

Ø Use points to specify exact location.

Lines

Ø A line is 1Dimensional, having length but no width or height.

Ø Lines are determined by 2 points

Planes

Ø 2dimensional flat surface, having length and width but without height.

Ø It extends on all sides, composed with an infinite number of points and lines

Intersection lines

Ø Lines or line segments that meet or cross at a certain point

Angles

Ø When 2 lines meet at a point (the end), they will make a certain angle.

Ø Every angles are not always the same

• In a circle, a radius perpendicular to a chord bisects the chord.
• a radius that bisects a chord is perpendicular to the chord.
• the perpendicular bisector of a chord passes through the center of the circle.

Intersecting Chords Rule

: (segment piece)×(segment piece) = (segment piece)×(segment piece)

Secant-secant rule:

: (whole secant)×(external part) = (whole secant)×(external part)

Secant-tangent rule

: (whole secant)×(external part) = (tangent)2

ANGLE PROPERTIES 

 The angle at the center is twice bigger of the angle at the circumference.

Both angles are in the same size.

 It's 90 degree, if we prove using the theory above.

Resources:

http://www.mathgoodies.com/lessons/vol2/geometry.html

https://www.mathsisfun.com/definitions/circle.html

http://www.math.com/tables/geometry/surfareas.htm

http://mathschallenge.net/library/geometry/angle_properties