Question

Fred and Victoria provide the following proofs for vertical angles to be equal.

Fred's proof: angle 2 + angle 3 = 180Á (t is a straight line)
angle 1 + angle 2 = 180Á (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 = 180Á (t is a straight line)
angle 1 + angle 2 =180Á (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

Answer 1

Both Fred and Victoria's proofs are correct.

Explanation:

Fred's proof:

• angle 2 + angle 3 = 180° (t is a straight line) IT IS TRUE THAT t IS A STRAIGHT LINE

• angle 1 + angle 2 = 180° (PQ is a straight line) IT IS TRUE THAT PQ IS A STRAIGHT LINE

• Therefore, angle 1 + angle 2 = angle 2 + angle 3 (Transitive Property of Equality) THIS IS AN EXAMPLE OF THE TRANSITIVE PROPERTY OF EQUALITY

• Hence, angle 1 = angle 3 (Subtraction Property of Equality)THIS IS AN EXAMPLE OF THE SUBTRACTION PROPERTY OF EQUALITY

Victoria's proof:

• angle 1 + angle 4 = 180° (t is a straight line) TRUE

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

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

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

Answer 2

Both Fred and Victoria are correct.