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Chapter 2: Q8 (page 41)

Copy everything shown and supply missing statements and reasons.

Given:FL=AT

Prove: FA=LT

Proof:

Short Answer

Expert verified

By reflexive property, LA=LA.

Step by step solution

01

Step 1. Apply the reflexive property of congruence.

By reflexive property, LA=LA.

02

Step 2. Addition property of algebra.

If a=band c=d, then a+c=b+d.

03

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

04

Step 4. Apply segment addition postulate.

From the given figure, it can be observed that some of FLand LAgives FAand the sum of LAand ATgives LT, that is,

FL+LA=FA;LA+AT=LT

05

Step 5. Substitution property.

Substitute FAfor FL+LAand LTfor LA+ATinto step 3.

FL+LA=AT+LAFA=LT

Hence, it is proved that FA=LT.

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