1. 2.5 Proofs Segments and Angles

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

3. 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

4. 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.

5. 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.

6. 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

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