Question

Can someone help me with this asap please, thanks!

Answer 1

Given:
`r\perp s` and
`t\perp s`.

Prove:
`r\parallel t`

Since
`r\perp s`, By the definition of perpendicular lines angles 1, 2, 3 and 4 are 90 degree. similarly
`t\perp s`, it means angles 5, 6, 7 and 8 are 90 degree.

We can say that,

`\angle 1\cong \angle 5`,
`\angle 2\cong \angle 6`,
`\angle 3\cong \angle 7` and
`\angle 4\cong \angle 8`

From figure it is noticed that the angle 1 and 5 are corresponding angles.

If two parallel lines are intersected by a transversal, then the corresponding angles are equal.

Since corresponding angles are congruent, therefore the line must be parallel to each other.

Hence proved that
`r\parallel t`.