EF + FG = EG
A Transitive Property
B Multiplication Property
C Addition Property
D Simplify
E Angle Addition Postulate
F Substitution
GSubtraction Property
H Divison Property
I Segment Addition Postulate
C Addition Property
Based on the given equation EF + FG = EG, here is a breakdown of the properties involved:
1. Addition Property (C): This property states that you can add equal quantities to both sides of an equation without changing its validity. In this case, EF and FG are added together to get EG.
2. Substitution (F): This property allows you to substitute one value or expression for another. Here, the value of FG is replaced with EF + FG in the equation.
3. Simplify (D): This step involves simplifying the equation or expression by combining like terms. In this case, no further simplification is necessary.
4. Angle Addition Postulate (E): This postulate states that if point G lies on the interior of angle DEF, then the measure of angle DEF is equal to the sum of the measures of angle DEG and angle GEF.
Therefore, the correct sequence of properties used in the equation EF + FG = EG is:
C (Addition Property) -> F (Substitution) -> E (Angle Addition Postulate)
To solve the equation EF + FG = EG, we can determine which property or postulate was used to arrive at the result EG.
The Transitive Property states that if a = b and b = c, then a = c. However, this property does not involve addition or subtraction operations, so it does not apply in this case (option A can be eliminated).
The Multiplication Property states that if a = b, then ac = bc. Again, this property does not involve addition or subtraction operations, so it does not apply here (option B can be eliminated).
The Addition Property states that if a = b, then a + c = b + c. This property involves addition, but it does not explain how the equation was simplified or rearranged (option C can be eliminated).
The Simplify option refers to simplifying the equation, which is not specified in the given equation (option D can be eliminated).
The Angle Addition Postulate is a property specific to angles in geometry and does not apply here (option E can be eliminated).
The Substitution property involves replacing one value with another, which could explain why EF and FG were replaced with EG (option F is a possible choice).
The Subtraction Property states that if a = b, then a - c = b - c. This property involves subtraction, but it does not explain how EF and FG were combined (option G can be eliminated).
The Division Property states that if a = b and c ≠ 0, then a/c = b/c. This property involves division, and again, it does not explain how the original equation was simplified or rearranged (option H can be eliminated).
Lastly, the Segment Addition Postulate states that if B is between A and C, then AB + BC = AC. This is the most appropriate option for the given equation, as EG represents the total length of EG, and EF + FG represents the sum of the lengths EF and FG (option I is a possible choice).
So, the most appropriate answer would be:
F. Substitution
I. Segment Addition Postulate