Question

Two lines a and b are intersected by a transversal c prove that a//b, if

NEED IN 15 min am giving ABOUT 50 POINTS
ANY CHEATIN ANSWERS R BANNED!!
Pls help

Answer 1

Because Alternate Interior angles are equal.

Explanation:

STEP - I:

`$ m \angle {5} = 3 . m \angle {\{3}\} $`

Reason:

This is the given data.

STEP - II:

It has multiplied and the reason is mentioned as well.

STEP - III:

`$ m \angle{3} + m \angle{5} $` = 45° + 135° = 180°

Reason:

It has substituted the value of
`$ m\angle{5} $` from the previous step. The sum of
`$ m\angle{3} $` and
`$ m \angle{5} $` is 180°.

STEP - IV:

`$ a \parallel b $`

Reason:

We calculated
`$ m\angle{5}` to be 135°.

Note that
`$ \angle {5} $` and
`$ \angle{6} $` are on the same line. That means their sum should be 180°.

i.e.,
`$ m\angle{5} + m\angle{6} $` = 180°.

`$ \implies $` 135° +
`$ m\angle{6} $` = 180°.

`$ \implies m\angle{6} = $` 45°.

One of the ways to prove
`$ a \parallel b $` is to check if alternate interior angles are equal.

Here,
`$ m\angle{3} $` and
`$ m \angle {6} $` are alternate interior angles and they are equal.

`$ \implies a \parallel b $`.