Question

complete the proof by choosing the correct
eason\. given: eh = gj, fh = hj. prove: ef = gh. statement: 1. eh = ef + fh. 2. gj = gh + hj. 3. eh = gj. 4. ef + fh = gh + hj. 5. fh = hj. 6. ef + hj = gh + hj. 7. ef = gh.

Explanation:

Step1: Segment - addition postulate

$EH = EF+FH$ (Segment - addition postulate states that if F lies on the line segment EH, then the length of EH is the sum of the lengths of EF and FH)

Step2: Segment - addition postulate

$GJ = GH + HJ$ (Segment - addition postulate states that if H lies on the line segment GJ, then the length of GJ is the sum of the lengths of GH and HJ)

Step3: Given

$EH = GJ$ (Given in the problem statement)

Step4: Substitution

$EF + FH=GH + HJ$ (Substitute $EH$ with $EF + FH$ and $GJ$ with $GH + HJ$ since $EH = GJ$)

Step5: Given

$FH = HJ$ (Given in the problem statement)

Step6: Substitution

$EF + HJ=GH + HJ$ (Substitute $FH$ with $HJ$ in the equation $EF + FH=GH + HJ$)

Step7: Subtraction property of equality

$EF = GH$ (Subtract $HJ$ from both sides of the equation $EF + HJ=GH + HJ$)

Answer:

$EF = GH$