Chapter 2.6 Notes: Prove Statements about Segments and Angles

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Presentation transcript:

Chapter 2.6 Notes: Prove Statements about Segments and Angles Goal: You will write proofs using geometric theorems.

A proof is a logical argument that shows a satement is true. Two-Column Proofs: A two-column proof has numbered statements and corresponding reasons that show an argument in a logical order. In a two-column proof, each statement in the left-hand column is either given information or the result of applying a known property or fact to statements already made.

Each reason in the right-hand column is the explanation for the corresponding statement. Writing a Two-Column Proof: In a proof, you make one statement at a time, until you reach the conclusion. You are using deductive reasoning when you make statements based on facts.

Given: Prove: Statements: Reasons: 1. Given 2. 2. Angle Addition Post. 3. 3. Substitution Property 4. 4. Angle Addition Post. 5. 5. Transitive Property

Theorems: The reasons used in a proof can include definitions, properties, postulates, and theorems. A theorem is a statement that can be proven.

Ex. 1: Write a two-column proof Ex.1: Write a two-column proof. Given: M is the midpoint of Prove: AM =

Ex.2: Write a two-column proof. R S T U Given: RT = SU Prove: RS = TU

Ex.3: Write a two-column proof.

Ex.4: Write a two-column proof.

Ex.5: Walking down a hallway at the mall, you notice the music store is halfway between the food court and the shoe store. The shoe store is halfway between the music store and the bookstore. Prove that the distance between the entrances of the food court and the music store is the same as the distances between the entrances of the shoe store and the bookstore.

Ex.6: The distance from the park to the pool is the same as the distance from your house to the school. the school is between the pool and the house. Prove that the distance from the park to the school is the same as the distance from the pool to your house.