Question

given: eg = hk, fg = hj. prove: ef = jk. step statement 5 ef + fg = hj + jk 6 ef + fg = hj + jk substitution property substitution property 7 reason? validate send to proof send to proof send to proof

Explanation:

Step1: Recall segment - addition postulate

By the segment - addition postulate, $EG=EF + FG$ and $HK=HJ + JK$.

Step2: Use the given equalities

Since $EG = HK$ (given), we can substitute $EG$ with $EF + FG$ and $HK$ with $HJ + JK$ using the substitution property, getting $EF+FG=HJ + JK$.

Step3: Use the given equalities again

Given $FG = HJ$, substitute $FG$ with $HJ$ in the equation $EF+FG=HJ + JK$. After substitution, we can subtract $HJ$ from both sides of the equation.
$EF+HJ=HJ + JK$ (substitution of $FG$ with $HJ$), then $EF=JK$ (subtraction property of equality).

Answer:

The reason for step 7 (to get $EF = JK$ from $EF+FG=HJ + JK$ and $FG = HJ$) is the Subtraction Property of Equality.