2.5 Proofs Segments and Angles

What we will learn Writing two column proofs Name properties of congruence

Needed vocab Proof: logical argument that uses deductive reasoning to show that a statement is true Two column proof: numbered statements and corresponding reasons that show an argument in logical order Theorem: statement that can be proven

Exs. 1, 3, and 4 Two column Proofs Statement Reason 1. 𝑚∠1=𝑚∠3 2. 𝑚∠𝐷𝐵𝐴=𝑚∠3+𝑚∠2 3. 𝑚∠𝐷𝐵𝐴=𝑚∠1+𝑚∠2 4. 𝑚∠1+𝑚∠2=𝑚∠𝐸𝐵𝐶 5. 𝑚∠𝐷𝐵𝐴=𝑚∠𝐸𝐵𝐶 1. Given 2. Angle Add (Post 1.4) 3. Substitution 4. Angle Add (Post 1.4) 5. Transitive prop.

More Practice Statement Reason Do page 103 #13 1. ∠𝐺𝐹𝐻≅∠𝐺𝐻𝐹 2. ∠𝐸𝐹𝐺 𝑎𝑛𝑑 ∠𝐺𝐹𝐻 𝑎𝑟𝑒 𝑠𝑢𝑝𝑝 3. m∠𝐸𝐹𝐺+𝑚∠𝐺𝐹𝐻=180 4. m∠𝐸𝐹𝐺+𝑚∠𝐺𝐻𝐹=180 5. ∠𝐸𝐹𝐺 𝑎𝑛𝑑 ∠𝐺𝐹𝐻 𝑎𝑟𝑒 𝑠𝑢𝑝𝑝 1. Given 2. Definition of linear pair 3. Definition of supp 4. Substitution Prop 5. Definition of supp.

Your Practice Statement Reason Do page 103 #14 1. 𝐴𝐵≅𝐹𝐺, 𝐵𝐹 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 𝐴𝐶 𝑎𝑛𝑑 𝐷𝐺 2. 𝐵𝐶≅𝐴𝐵, 𝐹𝐺≅𝐷𝐹 3. 𝐵𝐶≅𝐹𝐺 4. 𝐵𝐶≅𝐷𝐹 1. Given 2. Def. of Bisector 3. Transitive Prop 4. Transitive Prop

Ex. 2 Naming Properties If ∠ 𝑇 ≅∠𝑉and ∠𝑉≅∠𝑅, then ∠𝑇≅∠𝑅 Transitive prop If JL≅YZ, then YZ≅JL Symmetric prop