Angles – measurement, construction, estimation

When two lines meet at a point, they make an angle. The two lines are called the arms of the angle and the point is called the vertex.

Detailed description

Two angles are created. One angle falls inside the arms, and the other angle falls outside them.

Detailed description

To measure the angle we see how much one of the lines must be turned through the shaded area to get to the other line.
An understanding of angles forms the basis of much of the geometry you will meet in upper primary and in secondary school. Geometry, including angles, has been used throughout history. The Egyptians must have had a very good knowledge of angles to construct the pyramids so perfectly.

Measuring and Constructing Segments

Definitions:

Distance - The distance between any two points is the absolute value of the difference of the coordinates.
Length - The distance between two points.
Congruent segments - Segments that have the same length.
Coordinates - A point on a grid or graph.
Construction - A way of creating a figure that is more precise.
Midpoint - The point that bisects or divides the segment into two congruent segments.

Examples

Understanding points, lines and planes

Undefined TermsPoint: names a location and has no size(a capital letter is expressed with a dot).
Line: is a straight path that has no thickness and extends forever(a lowercase letter or two points on a line).
Plane: a flat surface that has no thickness and extends forever( a script capital letter or three points not on a line).
Collinear: points that lie on the same line(see pictures at the bottom).
Coplanar: points that lie on the same plane( see pictures at the bottom).
Segment and Rays:Segment: line segment, is the part of a line consisting of two points and all points between them.
Endpoint: is a point at one end of a segment or the starting point of a ray.
Ray: is a part of a line  that starts  at an endpoint and extends forever in one direction.
Postulates( statement excepted without proof)-Lines, Points, and Planes.
1-1-1 Through any two points there is exactly one line.
1-1-2 Through any three noncollinear points there is exactly one plane containing them.
1-1-3 If two points lie in a plane, then the line containing those points lies in the plane
Postulates- intersections of lines and planes.
1-1-4 If two lines intersect, then they intersect in exactly one point.
1-1-5 If two planes intersect, then they intersect in exactly one line.