Question

prove that if a transversal intersect two Parallel Lines then each pair of alternate interion angles is equaror​

Answer 1

Given: Let PQ and RS are two parallel lines and AB be the transversal which intersects them on L and M respectively.

To Prove: ∠PLM = ∠SML

And ∠LMR = ∠MLQ

Proof: ∠PLM = ∠RMB ………….equation (i) (Corresponding ngles)

∠RMB = ∠SML ………….equation (ii) (vertically opposite angles)

From equation (i) and (ii)

∠PLM = ∠SML

Similarly, ∠LMR = ∠ALP ……….equation (iii) (corresponding angles)

∠ALP = ∠MLQ …………equation (iv) (vertically opposite angles)

From equation (iii) and (iv)

∠LMR = ∠MLQ Proved