Question

given: eg = hk, fg = hj. prove: ef = jk. 1. fg = hj (given) 2. ef + fg = eg (segment addition property) 3. fg + hj = hk (segment addition property) 4. ef - fg = eg (incorrect step, likely a typo should be ef + fg = eg as in step 2) 5. reason?

Explanation:

Step1: Recall given information

Given: $EG = HK$, $FG=HJ$

Step2: Apply segment - addition property

We know that $EG=EF + FG$ and $HK = HJ+JK$ (by segment - addition property). Since $EG = HK$ and $FG = HJ$, we can substitute these values into the equations: $EF+FG=HJ + JK$. Then, by subtracting $FG$ (which is equal to $HJ$) from both sides of the equation $EF+FG=HJ + JK$, we get $EF=JK$.

Answer:

The proof is completed by using the segment - addition property and substitution to show that $EF = JK$.