2. 2.5 Introduction to Proofs Proof: a convincing argument that uses deductive reasoning. A proof logically shows why a conjecture is true. Two-Column Proof: lists each statement on the left, and the justification or reason for the statement on the right.

3. Example 1: Write a two-column proof to justify the steps in solving the problem A 3(x+4) Z K3x Given: AK =42 Prove: ZK =15

4. Example 2: Write a two-column proof to justify the steps in solving the problem x° (3x + 20)° Given: ∠ CDE and ∠ EDF are supplementary Prove: m ∠ EDF = 140 C D E F

5. Example 3: Fill in the reasons to justify the statements. StatementsReasons 1. C is the midpoint of AD1. 2. AC ≅ CD 2. 3. AC = CD3. Congruent segments have equal length 4. 4x = 2x + 124. 5.5. Subtraction Property of Equality 6. x=66. A C D 4x 2x+ 12 Given: C is the midpoint of AD Prove: x = 6

6. AB C D E Given: m∠1 = m∠3 Prove: m∠AEC = m∠DEB 1 2 3 Example 4: Fill in the reasons to justify the statements. StatementsReasons 1. m ∠ 1 = m ∠ 3 1. 2. m ∠ BEC = m ∠ BEC 2. 3. m ∠ 1 + m ∠ BEC = m ∠ 3 + m ∠ BEC 3. 4. m ∠ 1 + m ∠ BEC = m ∠ AEC m ∠ 3 + m ∠ BEC = m ∠ DEB 4. 5. m ∠ 1 + m ∠ BEC = m ∠ AEC m ∠1 + m ∠ BEC = m ∠ DEB 5. 6. m ∠ AEC = m ∠ DEB 6.