Fred and victoria provide the following proofs for vertical angles to be equal:
a line pq is shown cut by a transversal t. 1, 2, 3, 4 are marked clockwise as the four angles formed by the transversal on the segment pq
fred's proof: angle 2 + angle 3 = 180° (t is a straight line)
angle 1 + angle 2 = 180° (pq is a straight line)
therefore, angle 1 + angle 2 = angle 2 + angle 3 (transitive property of equality)
hence, angle 1 = angle 3 (subtraction property of equality)
victoria's 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)
which statement is correct?
both fred's and victoria's proofs are correct.
both fred's and victoria's proofs are incorrect.
only fred's proof is correct.
only victoria's proof is correct.