Question

question 4 of 8 (1 point) | question attempt: 1 of 3
prove: ( de = fg )

statement	reason
2 ( fh = fg + gh )	segment addition property
3 ( dg cong fh )	given
4 ( de + eg = fg + gh )	substitution property
5 ( eg = gh )
6 ( de + gh = fg + gh )
7 ( de = fg )

reason options (for step 7): given, reflexive property, transitive property, addition and subtraction properties, multiplication and division properties, substitution property, definition of congruent segments, segment addition property, definition of congruent angles, angle addition property

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21-22 ppt earth...

Explanation:

Step1: Analyze the equation transformation

We have the equation \( DE + GH = FG + GH \). To get \( DE = FG \), we need to subtract \( GH \) from both sides of the equation. This is based on the Addition and Subtraction Properties of equality, which state that if we add or subtract the same quantity from both sides of an equation, the equation remains true.

Step2: Apply the property

Starting with \( DE + GH = FG + GH \), subtract \( GH \) from both sides:
\( DE + GH - GH = FG + GH - GH \)
Simplifying both sides (since \( GH - GH = 0 \) for the left - hand side and the same for the right - hand side), we get \( DE = FG \). So the reason for going from \( DE + GH = FG + GH \) to \( DE = FG \) is the Addition and Subtraction Properties.

Answer:

Addition and Subtraction Properties