Explanation:
The numbers are for the blanks. Some are statements; some are reasons.
1) Given (self-explanatory. Proofs often list all the given statements at their beginning.)
2) DE ≅ EF (a midpoint divides a segment into two congruent segments)
3) substitution property (equals can be substituted for equals)
4) Addition (or subtraction) property of equality (-2x is added to both sides)
5) 6 = 2x (1 is added to both sides)
6) 3 = x (both sides are divided by 2)
8) substitution property (2 can be substituted for x, since they are equal)
9) closure properties of multiplication and addition in real numbers*
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* have never been clear as to the property you invoke to be able to do ordinary arithmetic.
