Question

1. given: ∠1 ≅ ∠2

prove: a ∥ b
what is the missing statement in the proof?

statements | reasons

1. ∠1 ≅ ∠2 | 1. given
2. ? | 2. vertical angles are congruent.
3. ∠2 ≅ ∠4 | 3. transitive property of congruence
4. a ∥ b | 4. if two lines and a transversal form congruent corresponding angles, then the lines are parallel.

∠1 ≅ ∠2
a ⊥ b
a ∥ b
∠1 ≅ ∠4

Explanation:

Step1: Analyze the reason for statement 2

The reason for statement 2 is "Vertical angles are congruent". Vertical angles are the angles opposite each other when two lines cross. In the given diagram, \(\angle1\) and \(\angle4\) are vertical angles.

Step2: Determine the missing statement

Since vertical angles are congruent, the missing statement (statement 2) should be \(\angle1\cong\angle4\)

Answer:

\(\angle1\cong\angle4\) (the fourth option)