Question

if a transversal intersects two lines than a line are parallel if and only in each pair of alternate interior angles are same please solve properly​

Answer 1

Step-by-step explanation:

Given: AB and CD are two parallel lines and EF is a transversal which intersect them at M and N respectively forming two pairs of interior angles ∠1,∠3 and ∠2,∠4.

To Prove : (i) ∠1+∠3=180

or ∠2+∠4=180

Proof : Since ray ND stands on line EF,

∠3+∠5=180

.(i) (linear pair of angles)

But ∠1=∠5.(ii) (Corresponding angles as AB∣∣CD)

From (i) and (ii), we get

∠1+∠3=180

.(iii)

Again ray CN stands on EF,

∠2+∠6=180

(Linear pair of angles)

But ∠4=∠6 (Corresponding angles as AB∣∣CD)

⇒∠2+∠4=180

.(iv)

Hence, we can say if a transversal intersects two parallel lines, then each pair of interior angles are supplementary

i.e.∠1+∠3=180

prove ∠2+∠4=180