Question

(a) A transversal intersects two lines. Which condition would always make the ten lines parallel? (i) Vertically opposite angles are equal. (ii) Interior angles on the same side of the transversal are complementary. (iii) Alternate interior angles are equal. (iv) Corresponding angles are supplementary.
give reasons​

Answer 1

Answer:

Theorem 2 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.

Answer 2

Step-by-step explanation:

Theorem 2 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

lines & angles 3

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