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Expert-verified Found in: Page 41 ### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279 # Copy everything shown and supply missing statements and reasons.Given: $FL=AT$Prove: $FA=LT$ Proof:  See the 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 $FA=LT$. ### Want to see more solutions like these? 