Question

Adam and Darius provide the following proofs for vertical angles to be equal

Answer 1

Darius' proof: angle 1 + angle 4 = 180° (t is a straight line)

angle 1 + angle 2 = 180° (PQ is a straight line)

Therefore, angle 1 + angle 2 = angle 1 + angle 4 (Transitive Property of Equality)

Hence, angle 2 = angle 4 (Subtraction Property of Equality)

Explanation:

Darius' Proof is correct, as he correctly defines the transitive property of equality. Unlike Adam, who falsely uses the term.

Answer 2

Below is to complete the question above:

Adam’s proof: angle 1 + angle 2 + angle 3 + angle 4 = 360°
Therefore, angle 2 + angle 3 = 180°
Hence, angle 1 = angle 3

Darius’ proof: angle 1 + angle 4 = 180° (transversal t is a straight line)
angle 1 + angle 2 = 180° (PQ is a straight line segment)
Therefore, angle 1 + angle 2 = angle 1 + angle 4
Hence, angle 2 = angle 4

Choices are

Only Adam’s proof is correct.
Only Darius’ proof is correct.
Both Adam’s and Darius’ proofs are correct.
Both Adam’s and Darius’ proofs are incorrect.

Answer is Adam's conclusion that angle 2 plus angle 3 is 180 is true, but unsupported. Further, the final conclusion is unsupported. Darius' proof is correct.