Revision Notes on Line and Angle
Learning Goal
1. Types of Lines
– Parallel lines
– Perpendicular lines
– Intersecting lines
2. Angle Relationships:
– Corresponding angles
– Alternate interior angles
– Alternate exterior angles
– Consecutive interior angles
Pairs of Lines
1. Intersecting Lines
If two lines cut each other than they are called intersecting lines.
That common point is called a Point of Intersection.
Here, line ‘l’ and ‘m’ intersect each other at point C.
2. Transversal
If a line intersects two or more lines at different points, then that line is called Transversal Line.
3. Parallel Lines
If perpendicular distance between the two lines at any point is same than they are called parallel lines.
Parallel Lines never meet with each other.
3. Angles made by a transversal
When a transversal intersects two lines then they make 8 angles.
Some of the angles made by transversal-
|
Types of Angles |
Angles shown in figure |
|
∠6, ∠5, ∠4, ∠3 |
|
∠7,∠8,∠1,∠2 |
|
∠1 and ∠5,∠2 and ∠6, ∠3 and ∠7,∠4 and ∠8 |
|
∠3 and ∠6,∠4 and ∠5 |
|
∠1 and ∠8,∠2 and ∠7 |
|
∠3 and ∠5,∠4 and ∠6 |
Transversal of Parallel Lines
The two lines which never meet with each other are called Parallel Lines. If we have a transversal on two parallel lines then-
a. All the pairs of corresponding angles are equal.
∠3 = ∠7
∠4 = ∠8
∠1 = ∠5
∠2 = ∠6
b. All the pairs of alternate interior angles are equal.
∠3 = ∠6
∠4 = ∠5
c. The two Interior angles which are on the same side of the transversal will always be supplementary.
∠3 + ∠5 = 180°
∠4 + ∠6 = 180°
Checking for Parallel Lines
This is the inverse of the above properties of the transversal of parallel lines.
Example: 1
If AB ∥ PQ, Find ∠W.
Solution:
We have to draw a line CD parallel to AB and PQ passing through ∠W.
∠QPW = ∠PWC = 50° (Alternate Interior Angles)
∠BAW =∠CWA = 46°(Alternate Interior Angles)
∠PWA = ∠PWC +∠CWA
= 50°+ 46°= 96°
Example: 2
If XY ∥ QR with ∠4 = 50° and ∠5 = 45°, then find all the three angles of the ∆PQR.
Solution:
Given: XY ∥ QR
∠4 = 50° and ∠5 = 45°
To find: ∠1, ∠2 and ∠3
Calculation: ∠1 + ∠4 + ∠5 = 180° (sum of angles making a straight angle)
∠1 = 180°- 50°- 45°
∠1 = 85°
PQ is the transversal of XY and QR, so
∠4 = ∠2 (Alternate interior angles between parallel lines)
∠2 = 50°
Pr is also the transversal of XY and QR, so
∠5 = ∠3 (Alternate interior angles between parallel lines)
∠3 = 45°