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Lines and Angles

In geometry, the word "line" refers to a straight line that extends without end in both directions.    



The part of the line from P to Q is called a line segment.  P and Q are the endpoints of the segment.  The notation PQ is used to denote both the segment and the length of the segment.  The intention of the notation can be determined from the context.  

\Intersecting Lines And Angles: If two lines intersect, the opposite angles are called vertical angles and have the same measure.  In the figure

PRQ and SRT are vertical angles and QRS and PRT are vertical angles. Also, x + y = 180 since PRS is a straight line.

Perpendicular Lines

If two lines intersect at right angles, the lines are perpendicular. 

For example:  



A right angle symbol in an angle of intersection indicates that the lines are perpendicular. 

Parallel Lines

If two parallel lines are intersected by a third line, as shown below, then the angle measures are related as indicated, where x + y = 180.    



• An angle greater than 180°, but less than 360° is called a reflex angle.                                 

• Two angles whose sum is 90° are called complementary angles.

• Two angles having a sum of 180° are called supplementary angles.


When two lines intersect, two pairs of vertically opposite angles are equal. 
The sum of 2 adjacent angles is 180°. 


As given in the above diagram A = C & B = D. Secondly A + B =180°C + D =180° 


Two lines are parallel to each other if

• They are parallel to a 3rd line.

• They are opposite sides of a rectangle/square/rhombus/parallelogram.

• If they are perpendicular to a 3rd line.

• If one of them is a side of the triangle & other joins the midpoints of the remaining two sides.

• If 1 of them is a side of a triangle & other divides other 2 sides proportionately.


Two lines are perpendicular to each other if

• They are arms of a right-angle triangle.

• If the adjacent angles formed by them are equal and supplementary.

• They are adjacent sides of a rectangle or a square.

• If they are diagonals of a rhombus.

• If one of them is a tangent & other is radius of the circle through the point of contact.

• If the sum of their squares is equal to the square of line joining their ends.

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