Chapter 5 Lines and angles discusses the various angles formed when two lines meet. Before we get into this discussion, let us recall the following terminologies.
- Line Segment – Part of the line bounded by two distinct end points. If we extend the two endpoints in either direction endlessly, we get a line.
In the given image, (i) represents a line segment, (ii) represents a line and (iii) represents a ray.
- Angle – When two line segments meet, an angle is formed. The angles are classified as an acute, obtuse and right angle.
Apart from this classification, there are related angles. Related angles are a pair of angles that are given specific names. The various types of related angles are:
- Complementary Angles – When the sum of two angles is 90°, the angles are known as complementary angles.
- Supplementary Angles – When the sum of two angles is 180°, the angles are known as supplementary angles.
- Adjacent Angles – The pair of angles that have a common vertex and an arm is known as adjacent angles. They have non-common arms are on either side of the common arm.
- Linear Pairs – Pair of adjacent angles whose non-common sides are opposite rays.
- Vertically Opposite Pair -The angles opposite to each other when two lines meet.
Pair of Lines
- When two lines meet, we say that it intersects. The point at which they meet is known as the point of intersection.
- When two lines don’t meet, however far produced, they are known as parallel lines.
- A line that intersects two or more lines at distinct points is known as transversal. A transversal gives rise to many angles. The various angles formed are given below in the table.
|Interior Angles||∠3, ∠4, ∠5, ∠6|
|Exterior Angles||∠1, ∠2, ∠7, ∠8|
|Pair of Corresponding Angles||∠1 and ∠5, ∠2 and ∠6,
∠3 and ∠7, ∠4 and ∠8
|Pair of Alternate Interior Angles||∠3 and ∠6, ∠4 and ∠5|
|Pair of Alternate Exterior Angles||∠1 and ∠8, ∠2 and ∠7|
|Pair of Interior Angles on the same side of the transversal||∠3 and ∠5, ∠4 and ∠6|
The following relationships are observed when a transversal cuts two parallel lines.
- Each pair of corresponding angles are equal
∠1 = ∠5, ∠3 = ∠7, ∠2 = ∠6, ∠4 = ∠8
- Each pair of alternate interior angles are equal.
∠3 = ∠6, ∠4 = ∠5
- Each pair of interior angles on the same side of the transversal are supplementary.
∠3 + ∠5 = 180°, ∠4 + ∠6 = 180°
Class 7 Maths Lines And Angles Questions
- An angle is greater than 45º. Is its complementary angle greater than 45º or equal to
45º or less than 45º?
- In the given figure,
- Is ∠1 adjacent to ∠2?
- Is ∠AOC adjacent to ∠AOE?
- Do ∠COE and ∠EOD form a linear pair?
- Are ∠BOD and ∠DOA supplementary?
- Is ∠1 vertically opposite to ∠4?
- What is the vertically opposite angle of ∠5?
- In the given image, is ∠1 adjacent to ∠2? Give reasons.
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