Question

Can someone help me with this asap please, thanks!

Answer 1

Answer:

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 $r\parallel t$.