Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
Point: A fine dot made by a sharp pencil on a sheet of paper.
Line: Fold a piece of paper, the crease in the paper represents a line. A line can be extended to any length on both sides. It has no end points. A line has no breadth and named using any two points on it i.e. AB or by a single small letter l or m or n.
Line Segment: The portion of the line between two points A and B is called a line segment. A line segment has two end points.
Ray: A line segment AB when extended in one direction. Ray has one end point, called the initial point.
Plane: A flat surface, which extends indefinitely in all directions. For example, surface of smooth wall, sheet of a paper.
Point and Line
An infinite number of lines can be drawn through a point. All lines are called concurrent lines.
One and only one line can be drawn passing through two given points.
If a line can pass through three or more points, then these points are said to be collinear otherwise points are non-collinear. Two distinct lines can not have more than one point in common.
Two lines in the same plane are called parallel lines if both have no points in common or if the distance between the lines is same everywhere.
Angles
Angle is formed by two rays with a common initial point called vertex and measured in degrees.
- Acute angle: An angle whose measure is less than 90º.
- Right angle: An angle whose measure is 90º.
- Obtuse angle: An angle whose measure is more than 90º but less then 180º.
- Straight angle: An angle whose measure is 180º. Angle obtained by two opposite rays is called a straight angle.
- Reflex angle: An angle whose measure is more than 180º and less than 360º.
Two lines or rays making a right angle with each other are called perpendicular lines.
Pairs of Angles
Complementary angles: Two angles are said to be complementary to each other if the sum of their measures is 90º.
Supplementary angles: Two angles are said to be supplementary if the sum of their measures is 180º.
Adjacent angles: Two angles having a common vertex, a common arm and non-common arms on opposite sides of the common arm. ∠BAC and ∠CAD are a pair of adjacent angles with common vertex A and common arm AC.
Linear Pair: If AB and AC are opposite rays and AD is any other ray then ∠BAD and ∠CAD are said to form a linear pair.
Vertically opposite angles: Two angles are called a pair of vertically opposite angles, if their arms form two pairs of opposite rays. ∠AOC and ∠BOD, ∠AOD and ∠COB are pairs of vertically opposite angles.
When a transversal intersects two parallel lines, then
- each pair of corresponding angles are equal.
- each pair of alternate angles are equal.
- each pair of interior angles on the same side of the transversal are supplementary.