0Lines and Angles – Definitions & Properties
Line segment: A line segment has two end points with a definite length.
Ray : A ray has one end point and infinitely extends in one direction.
Straight line : A straight line has neither starting nor end point and is of infinite length.
Acute angle : The angle that is between 0° and 90° is an acute angle.
Obtuse angle : The angle that is between 90° and 180° is an obtuse angle.
Right angle : The angle that is 90° is a Right angle.
Straight angle : The angle that is 180° is a straight angle.
Supplementary angles : If the sum of two angles is 180° then the angles are called supplementary angles.
Two right angles always supplement each other.
Linear Pair : The pair of adjacent angles whose sum is a straight angle is called a linear pair.
Complementary angles :
If the sum of two angles is 90° then the two angles are called complementary angles.
Adjacent angles :
The angles that have a common arm and a common vertex are called adjacent angles.
Vertically opposite angles :
When two lines intersect, the angles formed opposite to each other at the point of intersection (vertex) are called vertically opposite angles.
Perpendicular lines: When there is a right angle between two lines, the lines are said to be perpendicular to each other.
Parallel lines :
Here, A and B are two parallel lines, intersected by a line p.
The line p is called a transversal, that which intersects two or more lines (not necessarily parallel lines) at distinct points.
As seen in the figure above, when a transversal intersects two lines, 8 angles are formed.
When a transversal intersects two parallel lines,
1. The corresponding angles are equal.
2. The vertically opposite angles are equal.
3. The alternate interior angles are equal.
4. The alternate exterior angles are equal.
5. The pair of interior angles on the same side of the transversal is supplementary.
We can say that the lines are parallel if we can verify at least one of the aforementioned conditions.
Q.) Find the complementary and supplementary of 75°?
Q.) Guess the two angles which is equal and are supplementary to each other?
