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Vocabulary flowchart proof 2-column proof paragraph proof

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Example 1: Reading a Flowchart Proof

Use the given flowchart proof to write a two-column proof. Given: 2 and 3 are comp. 1 3 Prove: 2 and 1 are comp. Flowchart proof:

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Statements Reasons Example 1 Continued Two-column proof:

1. 2 and 3 are comp. 1 3 1. Given 2. m2 + m3 = 90° 2. Def. of comp. s 3. m1 = m3 3. Def. of s 4. m2 + m1 = 90° 4. Subst. 5. 2 and 1 are comp. 5. Def. of comp. s

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Example 2 Use the given flowchart proof to write a two-column proof. Given: RS = UV, ST = TU Prove: RT TV Flowchart proof:

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Statements Reasons Example 2 Continued 1. RS = UV, ST = TU 1. Given

2. RS + ST = TU + UV 2. Add. Prop. of = 3. RS + ST = RT, TU + UV = TV 3. Seg. Add. Post. 4. RT = TV 4. Subst. 5. RT TV 5. Def. of segs.

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Hw – Example 3 Use the given two-column proof to write a flowchart proof. Given: B is the midpoint of AC. Prove: 2AB = AC

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Hw – Example 4 Use the given two-column proof to write a flowchart proof. Given: 2 4 Prove: m1 m3 Two-column Proof:

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A paragraph proof is a style of proof that presents the steps of the proof and their matching reasons as sentences in a paragraph. Although this style of proof is less formal than a two-column proof, you still must include every step.

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Example 5: Reading a Paragraph Proof

Use the given paragraph proof to write a two-column proof. Given: m1 + m2 = m4 Prove: m3 + m1 + m2 = 180° Paragraph Proof: It is given that m1 + m2 = m4. 3 and 4 are supplementary by the Linear Pair Theorem. So m3 + m4 = 180° by definition. By Substitution, m3 + m1 + m2 = 180°.

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Statements Reasons Example 5 Continued Two-column proof:

1. m1 + m2 = m4 1. Given 2. 3 and 4 are supp. 2. Linear Pair Theorem 3. m3 + m4 = 180° 3. Def. of supp. s 4. m3 + m1 + m2 = 180° 4. Substitution

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Hw – Example 6 Use the given paragraph proof to write a two-column proof. Given: WXY is a right angle. 1 3 Prove: 1 and 2 are complementary. Paragraph Proof: Since WXY is a right angle, mWXY = 90° by the definition of a right angle. By the Angle Addition Postulate, mWXY = m2 + m3. By substitution, m2 + m3 = 90°. Since 1 3, m1 = m3 by the definition of congruent angles. Using substitution, m2 + m1 = 90°. Thus by the definition of complementary angles, 1 and 2 are complementary.

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Example 7: Writing a Paragraph Proof

Use the given two-column proof to write a paragraph proof. Given: 1 and 2 are complementary Prove: 3 and 4 are complementary m3 + m4 = 90° 3 and 4 are comp.

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Example 7 Continued Paragraph proof:

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Hw- Example 8 Use the given two-column proof to write a paragraph proof. Given: 1 4 Prove: 2 3 Two-column proof:

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Hw – Lesson Quiz Use the para proof to write a flowchart and 2-column proof. a paragraph proof

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