Question

question 5 of 5 what is the missing reason in the proof? given: ab ≅ cd cf ≅ eb prove: ae ≅ fd proof: ab ≅ cd given

Explanation:

Step1: State segment - addition postulate

$AB = AE + EB$ and $CD=CF + FD$

Step2: Use substitution

Since $AB\cong CD$ (given), then $AE + EB=CF + FD$

Step3: Use given congruence

Since $CF\cong EB$ (given), then $EB = CF$. Substitute $CF$ for $EB$ in $AE + EB=CF + FD$.
We get $AE+CF = CF + FD$

Step4: Apply subtraction property of equality

Subtract $CF$ from both sides of the equation $AE+CF = CF + FD$.
We have $AE=FD$, which means $AE\cong FD$

Answer:

$AE\cong FD$ is proved by using segment - addition postulate, substitution, and subtraction property of equality.