In the following proof

MATHEMATICS · Single correct · CBSE · Mathematics · Lines and Angles · Lines and Angles

Problem

In the following proof, lines l and m are intersected by a transversal t. Step 1: ∠1\angle 1 and ∠2\angle 2 are corresponding angles with respect to l, m and t. Step 2: ∠1=∠3\angle 1 = \angle 3 (given). Step 3: ∠3=∠2\angle 3 = \angle 2 (by the vertical angle theorem). Step 4: ______ Which of the following statements correctly completes Step 4 and therefore proves that l \u2225 m? (a) ∠1\angle 1 and ∠2\angle 2 are alternate interior angles, therefore l∥ml \parallel m. (b) ∠1+∠2=180∘\angle 1 + \angle 2 = 180^{\circ}, therefore l∥ml \parallel m. (c) ∠1=∠2\angle 1 = \angle 2, therefore l∥ml \parallel m. (d) ∠1=∠2\angle 1 = \angle 2, therefore l⊥ml \perp m.

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