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2-5Postulates and Paragraph Proofs Day 2
Write paragraph proofs
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Paragraph Proof A paragraph proof is one method of proving statements and conjectures. It involves writing a paragraph to explain why a conjecture for a given situation is true. Paragraph proofs are also called informal proofs. This does not mean that this form of proof is any less valid than the other types of proofs.
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Page 129 in your book.
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Write a paragraph proof
Given: Prove: ACD is a plane. Proof: and must intersect at C because if two lines intersect, then their intersection is exactly one point. Point A is on and point D is on Points A, C, and D are not collinear. Therefore, ACD is a plane as it contains three points not on the same line.
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Proof: ?
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Choose the best reason to complete the proof.
A. Definition of midpoint B. Segment Addition Postulate C. Definition of congruent segments D. Substitution
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Given that M is the midpoint of 𝑋𝑌 , write a paragraph proof to show that
𝑋𝑀 ≅ 𝑀𝑌 Given: M is the midpoint of 𝑋𝑌. Prove 𝑋𝑀 ≅𝑀𝑌 STEP 1 X M Y STEP 2 If M is the midpoint of 𝑋𝑌 , then from the definitions of midpoint of a segment, we know that XM + MY. This means that 𝑋𝑀 and 𝑀𝑌 have the same measure. By the definition of congruence, if two segments have the same measure, then they are congruent. Thus, 𝑋𝑀 ≅ 𝑀𝑌 . STEPS 3 & 4 STEP 5
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Once a conjecture is proven true, it can be states as a theorem and used in other proofs.
Therefore, a theorem is a conjecture that has been proven true. Page 129 in your book
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2-5 Assignment Day 2 Page 131, 34-42
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