Justify each step in the proof below (You may use a choice more than once. You will not use all the choices given. ) EG = 68 Image of line: E to F is 8x-12 and F to G is 2x Drawing not to scale. (5 points) Given : EG = 68 Prove: x = 8 1. EG = 68, EF = 8x-12, FG = 2x 1. Given 2. EF + FG = EG (2. Fill in the blank) 3. 8x - 12 + 2x = 68 (3. Fill in the blank) 4. 10x - 12 = 68 (4. Fill in the blank) 5. 10x = 80 (5. Fill in the blank) 6. x = 8 (6. Fill in the blank) Choices: Transitive Property, Substitution, Subtraction Property, Simplify, Multiplication Property, Segment Addition Postulate, Divison Property, Angle Addition Postulate, Addition Property
1. Given: EG = 68 (Given statement)
2. EF + FG = EG (Segment Addition Postulate)
3. 8x - 12 + 2x = 68 (Substitution)
4. 10x - 12 = 68 (Simplify)
5. 10x = 80 (Addition Property)
6. x = 8 (Division Property)