Anyone have another way of doing this proof? Like all given are in the first step.

Question

Given: AB≅BC

DE bisects AB

DE bisects BC

Prove: BD≅BE B AB and BC are segments

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/ \

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D /___ _\ E

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A /________\ C

Answer 1

Try it this way...

AD = DB and EC=BE <-- definition of bisector

AB = BC <-- given

AD+DB = BE + EC <-- line segment addition postulate

DB + DB = BE + BE <-- substitution

2*DB = 2 * BE <--- CLT

DB = BE <-- divides both sides by 2

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Step 1: AB=BC; All given

DE bisects AB;

DE bisects BC;

Step 2: AB = AD + DB and line segment addition postulate

CB = CE + EB

Step 3: AD=DB and CE = EB defintion of bisector

Step 4: AD + DB = CE + EB substitution

Step 5: BD + DB = BE + EB substitution

Step 6: 2*DB = 2*BE combines like terms; symmetric

Step 7: BD = BE division property of equality;

symmetric

Answer 2

There is nothing to prove!

The hypotheses indicate DC bisects both AB and BC...end of story!