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Chapter 2: Reasoning and Proof

Chapter 2: Reasoning and Proof. 2.6.1 Prove Statements about Segments and Angles. The 2 Column Proof and Theorems. A Proof is a logical Argument that shows a statement is true, a 2 Column Proof has numbered statements and corresponding reasons that show an argument in logical order

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Chapter 2: Reasoning and Proof

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  1. Chapter 2: Reasoning and Proof 2.6.1 Prove Statements about Segments and Angles

  2. The 2 Column Proof and Theorems • A Proof is a logical Argument that shows a statement is true, a 2 Column Proof has numbered statements and corresponding reasons that show an argument in logical order • The reasons used in a proof can be definitions, properties, postulates, and theorems • Atheorem is a statement that can be proven true, once proven a theorem can be used to prove other theorems

  3. R,S,T property applications • Congruence of Segments Theorem • Reflexive – • Symmetric – • Transitive - • Congruence of Angles Theorem • Reflexive – • Symmetric – • Transitive -

  4. Develop a proof • Given: QS is an angle bisector of PQR • Prove: mPQS = ½ mPQR Statements Reasons • QS is an angle bisector of PQR Given • PQS  SQR Definition of Angle Bisector • mPQS = mSQRDefinition of Congruent Angles • mPQS + mSQR = mPQR Angle Addition Postulate • mPQS + mSQR = mPQRSubstitution Property of Equality • 2 mPQS = mPQR Distributive Property • mPQS = ½ mPQRDivision Property of Equality

  5. Homework • pp. 116 • 1 – 11, 16, 17, 18, 23, 24, 26

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