Quick Review: Plane Geometry

There are different terms used in geometry. They are:

Point
  • It is a mark of position and has an exact location.
  • It has no thickness, length or breadth.
Line
  • A straight path that can be extended indefinitely in both the directions.
  • It doesn’t have a fixed length.
  • It has no fixed end points.
  • Infinite number of points lies on the line.
Ray
  • A straight path which can be extended indefinitely in one direction, keeping the other end fixed.
  • The fixed point (end point) is known as initial point.
  • It has no fixed length.
  • Infinite number of points lies on a ray.
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Line Segment
  • A straight path with a definite length.
  • It has two end points.
  • It is a part of a line.
  • Two line segments are said to be equal if they have the same length.
Parallel Lines
  • When two lines have no point in common, then they are said to be parallel lines.
  • The distance between the two parallel lines remains constant throughout.
Intersecting Lines
  • Two lines having a common point are said to be intersecting lines.
  • Two lines can intersect at most at one point only.
Collinear Points
  • Two or more points, lying on the same plane in a line are said to be collinear points.
  • The line is called "line of colinearity".
  • Two points on a line are always collinear.
Concurrent Lines
  • Three or more lines are said to be concurrent if there is a point which lies on all of them.
  • The common point is called the point of concurrence.
Angles
There are various types of angles. They are:
  • Right Angle
    When the angle is of 90°, it is called right angle
  • Acute Angle
    When the angle is less than 90°, it is known as acute angle.
  • Obtuse Angle
    When the angle is greater than 90° but less than 180°, it is called obtuse angle.
  • Reflex Angle
    When the angle is more than 180° but less than 360°, it is called reflex angle.
  • Straight Angle
    When the angle is of 180°, it is called straight angle.
  • Complete Angle
    When the angle is of 360°, it is known as complete angle.
  • Complementary Angles
    When the sum of measures of two angles is 90°, they are said to be complementary angles. Eg., 30° and 60° is a pair of complementary angles.
  • Supplementary Angles
    When the sum of measures of two angles is 180°, they are said to be supplementary angles. Eg., 75° and 105° is a pair of supplementary angles.
  • Adjacent Angles
    Two angles are said to be adjacent if:
    • They have same vertex
    • They have a common arm
    • Uncommon arms are on the either side of the common arm
  • Vertically Opposite Angles
    When two lines intersect, four angles are formed. The angles opposite to each other are called vertically opposite angles.
  • Linear Pair
    Two adjacent angles form a linear pair of angles, when their non-common arms are two opposite rays.
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Important Points

If two parallel lines are intersected by a transversal, then

  • Each pair of corresponding angles is equal.
  • Each pair of alternate angles is equal.
  • Interior angles on the same side of the transversal are supplementary.