Diana and Joby wrote the following proofs to prove that vertical angles are congruent. Who is correct?. . Diana’s Proof. . State
ment 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 .
2 answers:
The <em>correct answer</em> 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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