Question

Copy everything shown and supply missing statements and reasons.

Given:$FL=AT$

Prove: $FA=LT$

Proof:

Short answer

By reflexive property, $LA=LA$.

Step-by-step solution

Step 1. Apply the reflexive property of congruence.

By reflexive property, $LA=LA$.

Step 2. Addition property of algebra.

If $a=b$and $c=d$, then $a+c=b+d$.

Step 3. Description of step.

Use given information and step 1 and apply the addition property of algebra mentioned in step 2.

$FL+LA=AT+LA$

Step 4. Apply segment addition postulate.

From the given figure, it can be observed that some of $FL$and $LA$gives $FA$and the sum of $LA$and $AT$gives $LT$, that is,

$\begin{array}{c}FL+LA=FA;\\ LA+AT=LT\end{array}$

Step 5. Substitution property.

Substitute $FA$for $FL+LA$and $LT$for $LA+AT$into step 3.

$\begin{array}{c}FL+LA=AT+LA\\ FA=LT\end{array}$

Hence, it is proved that $FA=LT$.