What are line segment and a ray?
A line segment is a portion of a line with two endpoints whereas a ray is a line with just one endpoint. Three or more points are said to be collinear points if they lie on the same straight line. In all other conditions, the points will be termed as non-collinear points. Lines and angles class 9 notes discusses these concepts in a detailed manner.
What is an angle?
An angle is formed when 2 rays originate from the same point. There are basically 5 types of angles:
- Acute Angle
- Obtuse Angle
- Right Angle
- Reflex Angle
- Straight Angle
The angles measuring between 0 degrees to 90 degrees are called acute angles.
If an angle is exactly equal to 90 degrees then it is termed as a right angle.
An obtuse angle is always greater than 90 degree and less than 180 degrees.
The angles measuring exactly equal to 180 degrees are termed as straight angles.
A reflex angle is always greater than 180 degree but less than 360 degree.
Properties of Angles
- If the sum of two angles is 90 degree then those angles are called complementary angles, whereas in the case of supplementary angles the sum of two angles is 180 degree.
- Two angles are adjacent if they have a common vertex, a common arm and their non-common arms are on different sides of the common arm.
- According to Linear pair axiom, the sum of adjacent angles of a ray standing on a line is 180° and vice-versa.
- Vertically opposite angles of lines intersecting each other are equal.
- Lines parallel to a given line are also parallel to each other.
- The sum of all three angles of a triangle is always 180 degree.
- In a triangle, the exterior angle is always equal to the sum of the 2 interior opposite angles.
Q.1) The lines PQ and RS in the figure intersect each other at point O. If ∠POR : ∠ROQ = 5 : 7. Find all the angles.
Q.2) The ray OS stands on a line POQ. Ray OT and ray OR are angle bisectors of ∠POS and ∠SOQ, respectively. If ∠POS = x, find ∠ROT.
Q.3) The lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE.
Q.4) The lines XY and MN in the given figure intersect at O. If ∠POY = 90° and a:b = 2:3, find c.
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