Fred and Victoria provide the following proofs for vertical angles to be equal.
2 answers:
Both Fred and Victoria are correct.
Answer:
Both Fred and Victoria's proofs are correct.
Step-by-step 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) <u>TRUE</u>
- angle 1 + angle 2 =180° (PQ is a straight line) <u>TRUE</u>
- Therefore, angle 1 + angle 2 = angle 1 + angle 4 (Transitive Property of Equality)<u> TRUE</u>
- Hence, angle 2 = angle 4 (Subtraction Property of Equality) <u>TRU</u>
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