Answer:
Given: [tex]r\perp s[/tex] and [tex]t\perp s[/tex].
Prove: [tex]r\parallel t[/tex]
Since [tex]r\perp s[/tex], By the definition of perpendicular lines angles 1, 2, 3 and 4 are 90 degree. similarly [tex]t\perp s[/tex], it means angles 5, 6, 7 and 8 are 90 degree.
We can say that,
[tex]\angle 1\cong \angle 5[/tex], [tex]\angle 2\cong \angle 6[/tex], [tex]\angle 3\cong \angle 7[/tex] and [tex]\angle 4\cong \angle 8[/tex]
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 [tex]r\parallel t[/tex].
