Diana and joby wrote the following proofs to prove that vertical angles are congruent. who is correct? . diana’s proof. statement justification . 1 + 2 = 180° definition of supplementary angles . 1 + 4 = 180° definition of supplementary angles . 1 + 2 = 1 + 4 transitive property of equality . . joby’s proof. statement justification . 2 = 4 vertical angles are congruent. 1 = 3 vertical angles are congruent. vertical angles are congruent. vertical angle theorem .

The correct answer is:

Diana is correct.

Explanation:

A diagram of the problem is attached. Since ∠1 and ∠2 form a straight line, they are supplementary angles; this means that ∠1 + ∠2 = 180°.

Using the same logic, ∠1 and ∠4 form a straight line, so ∠1 + ∠4 = 180°.

Using the transitive property (or substitution), ∠1 + ∠2 = ∠1 + ∠4.

The last step would be to subtract ∠1 from each side, leaving ∠2 = ∠4, which are vertical angles.

Joby's proof is incorrect because you cannot use a statement you are trying to prove in its own proof.

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