Suppose we are given,
two lines & a transversal
We know that
For parallel lines
 Corresponding angles are equal
 Alternate interior angles are equal
 Interior angles on same side of transversal is supplementary
 Alternate exterior angles are equal
But the opposite is true as well

If corresponding angles are equal,
Line are parallel

If alternate interior angles are equal,
lines are parallel

If sum of interior angles on same side of transversal is 180°,
lines are parallel.

If alternate exterior angles are equal,
lines are equal.
Let’s do some questions
Is l ∥ m ?
a
Here,
Here,
∠1 = ∠2 = 50°
For lines l & m,
With transversal p
∠1 & ∠2 are alternate interior angles.
And they are equal.
So, lines l & m are parallel
ea
Is l ∥ m ?
a
Here,
Here,
∠1 = ∠2 = 120°
For lines l & m,
With transversal p
∠1 & ∠2 are alternate interior angles.
And they are equal.
So, lines l & m are parallel
ea
Is l ∥ m ?
a
Here,
Here,
∠1 = ∠2 = 45°
For lines l & m,
With transversal p
∠1 & ∠2 are corresponding angles.
And they are equal.
So, lines l & m are parallel
ea
Is l ∥ m ?
a
Here,
∠1 = ∠2 = 100°
For lines l & m,
With transversal p
∠1 & ∠2 are corresponding angles.
And they are equal.
So, lines l & m are parallel
ea
Is l ∥ m ?
a
Here,
Here,
∠1 = ∠2 = 105°
For lines l & m,
With transversal p
∠1 & ∠2 are corresponding angles.
And they are equal.
So, lines l & m are parallel
ea
Is l ∥ m ?
a
Here
Here,
∠1 = ∠2 = 60°
For lines l & m,
With transversal p
∠1 & ∠2 are corresponding angles.
And they are equal.
So, lines l & m are parallel
ea
Is l ∥ m ?
a
Here
Here,
∠1 + ∠2 = 45° + 135°
= 180°
For lines l & m,
With transversal p
∠1 & ∠2 are interior angles on the same side of transversal
And they are supplementary
So, lines l & m are parallel
ea
Is l ∥ m ?
a
Here,
Here,
∠1 + ∠2 = 110° + 70°
= 180°
For lines l & m,
With transversal p
∠1 & ∠2 are interior angles on the same side of transversal
And their sum is 180°.
So, they are supplementary
So, lines l & m are parallel
ea
Is l ∥ m ?
a
Here,
Here,
∠3 = ∠2 (Vertically opposite angles)
∠3 = 135°
Now, ∠1 = ∠3 = 135°
For lines l & m,
With transversal p
∠1 & ∠3 are corresponding angles.
And they are equal.
So, lines l & m are parallel
ea
Is l ∥ m ?
a
Here,
Here,
∠3 = ∠2 (Vertically opposite angles)
∠3 = 115°
Now, ∠1 = ∠3 = 115°
For lines l & m,
With transversal p
∠1 & ∠3 are corresponding angles.
And they are equal.
So, lines l & m are parallel
ea
Is l ∥ m ?
a
Here,
Here,
∠1 ≠ ∠2
For lines l & m,
With transversal p
∠1 & ∠2 are alternate interior angles.
And they are not equal.
So, lines l & m are not parallel
ea
Is l ∥ m ?
a
Here,
Here,
∠1 ≠ ∠2
For lines l & m,
With transversal p
∠1 & ∠2 are corresponding angles.
But they are not equal.
So, lines l & m are not parallel
ea
Is l ∥ m ?
a
Here,
Here,
∠3 = ∠2 (Vertically opposite angles)
∠3 = 80°
≠ 100°
∴ ∠1 ≠ ∠3
For lines l & m,
With transversal p
∠1 & ∠3 are corresponding angles.
But they are not equal.
So, lines l & m are not parallel
ea
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