Question

31. Two lines are respectively perpendicular
to two parallel lines. Show that they are
parallel to each other.​

Answer 1

Step-by-step explanation:

According to the figure consider the two parallel lines m and n

we know that p⊥m andq⊥n

so we get

∠1=∠2=90

o

We know that m∥n and p is a transversal

from the figure we know that ∠1 and ∠3 are corresponding angles

so we get

∠1=∠3

We also know that

∠2+∠3=90

o

We know that ∠2 and ∠3 are corresponding angles when the transversal n cuts p and q

so we get p∥q

therefore, it is shown that the two lines which are perpendicular to two parallel lines are parallel to each other.