Given: ∠1 ≅ ∠2 Prove: a ∥ b What is the missing reason in the proof? - Corresponding angles are congruent. - Converse of the Corresponding Angles Postulate. - Alternate interior angles are congruent. - Transitive Property of Congruence.
Mathematics · Middle School · Thu Feb 04 2021
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In order to prove that line a is parallel to line b given that angle 1 is congruent to angle 2, the missing reason would be "Converse of the Corresponding Angles Postulate."
Here are the logical steps to the proof:
Step 1: Identify ∠1 and ∠2 as corresponding angles with respect to the line a and line b.
Step 2: Given the information states that ∠1 ≅ ∠2.
Step 3: Apply the Converse of the Corresponding Angles Postulate, which states that if two corresponding angles are congruent, then the two lines are parallel.
Step 4: Conclude that a ∥ b using the Converse of the Corresponding Angles Postulate.