Question

question 19 (3 points) write a justification for each step, proving that ef = gh, given that eg = fh. statement reason 1. eg = fh 1. given information 2 eg = ef + fg fh = fg + gh 2. 3 ef + fg = fg + gh 3. 4. ef = gh 4.

Explanation:

Step1: Segment - addition postulate

By the segment - addition postulate, if we have a line segment with points in between, the whole segment is the sum of its sub - segments. So, for line segment $EG$ with point $F$ in between, $EG = EF+FG$, and for line segment $FH$ with point $G$ in between, $FH = FG + GH$.

Step2: Substitution property of equality

Since $EG = FH$ (given) and $EG = EF+FG$ and $FH = FG + GH$, we can substitute $EG$ with $EF + FG$ and $FH$ with $FG+GH$ to get $EF + FG=FG + GH$.

Step3: Subtraction property of equality

Subtract $FG$ from both sides of the equation $EF + FG=FG + GH$. According to the subtraction property of equality, if $a + c=b + c$, then $a=b$. So, $EF=GH$.

Answer:

1. Segment - addition postulate
2. Substitution property of equality
3. Subtraction property of equality