Question

2)Prove that, The alternate angles formed by a transversal of two
parallel lines are of equal measures.​

Answer 1

Answer:

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Answer 2

Answer:

Theorem : If a transversal intersects two parallel lines, then each pair of alternate interior angles is equal.

Solution: 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