Justify each step in the proof below (You may use a choice more than once. You will not use all the choices given. )

Question

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

Answer 1

Here's the justification for each step in the proof:

1. EG = 68, EF = 8x-12, FG = 2x

- Given (Given information).

2. EF + FG = EG

- Segment Addition Postulate (The sum of the lengths of two segments is equal to the length of the whole segment).

3. 8x - 12 + 2x = 68

- Substitution (Substituting the values of EF and FG).

4. 10x - 12 = 68

- Simplify (Combining like terms on the left side).

5. 10x = 80

- Addition Property (Adding 12 to both sides of the equation).

6. x = 8

- Division Property (Dividing both sides by 10).

So, each step is justified by the corresponding property or postulate.

Answer 2

2. Segment Addition Postulate.

3. Substitution (Property of Equality).

4. Addition Property (of Equality).

5. Division Property (of Equality).