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Question

Given: AC and BD bisect each other.

Prove: BC≅AD.

All given are used in step 1

Answer 1

AC and BD bisect each other given

label point where two segments intersect E

AE = CE definition of segment bisector

BE = DE

m<AED = m<BEC vertical angles are equal

triangle ADE congruent to triangle CBE SAS

BE congruent to AD CPCTE (corresponding parts of congruent triangle are equal)