1. Given: E is between G and L
GE = 2x
EL = 3x
GL = 10
Prove: x = 2
Statement / Reason
1. E is between G and L / 1. Given
GE = 2x
EL = 3x
GL = 10
2. GE + EL = GL / 2. Segment addition postulate
3. 2x + 3x = 10 / 3. Substitution property of equality
4. 5x = 10 / 4. Combining like terms
5. ∴ x = 2 / 5. Division property of equality
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2. Given: E is the midpoint between D and F
DE = 12x
EF = 8x + 20
Prove: x = 5
Statement / Reason
1. E is the midpoint between D and F / 1. Given
DE = 12x
EF = 8x + 20
2. DE = EF / 2. Definition of midpoint
3. 12x = 8x + 20 / 3. Substitution property of equality
4. 4x = 20 / 4. Subtraction property of equality
5. ∴ x = 5 / 5. Division property of equality
I might post the rest later if I feel too unconfident.
