Cailyn knows that if two angles are vertical, they are congruent. She also knows that if two angles are congruent, then they have the same measure. She is given vertical angles 1 and 2, and she concludes that m∠1 = m∠2. What law of reasoning does she use?

Question

Mathematics

Dominic Mejia

26 September, 09:48

Cailyn knows that if two angles are vertical, they are congruent. She also knows that if two angles are congruent, then they have the same measure. She is given vertical angles 1 and 2, and she concludes that m∠1 = m∠2. What law of reasoning does she use?

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Answers (1)

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Jaylyn Archer · Answer 1

Answer: Law of syllogism

Step-by-step explanation:

Since she is given that ∠1 and ∠2 are vertical angles.

⇒∠1=∠2 [ Since she knows that if two angles are vertical, they are congruent. ]

⇒ m∠1 = m∠2[Since she knows that if two angles are congruent, then they have the same measure.]

Therefore by law of syllogism, if ∠1 and ∠2 are vertical angles then m∠1 = m∠2.

The law of syllogism is a valid argument form of deductive reasoning. It is similar to the transitive property of equality, which reads: if a = b and b = c then, a = c.