Question

Do you know Geometry answer ?​

Answer 1

Step-by-step explanation:

Let AB and CD be the two parallel lines and EF be the transversal which intersects them at M and N respectively, such that there are two pairs of interior angles formed. These interior angles are ∠1,∠3 and ∠2,∠4

To prove:

∠1+∠3=180 or ∠2+∠4=180

Proof:

Ray ND stands on line EF,

∠3+∠5=180 eq.1 (linear pair of angles)

But ∠1=∠5 eq.2 (corresponding anglles as AB||CD)

From eq.1 and eq.2,

∠1+∠3=180 eq.3

Again ray CN stands on EF,

∠2+∠6 = 180 (linear pair of angles)

But ∠4=∠6 (corresponding angles as AB||CD)

∠2+∠4=180

Hence, it is proved that transversal intersects two parallel lines and each pair of interior angles are supplementary