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Based on the diagram above, the following relations hold true.
△ABC∼△ACD | △ABC∼△CBD |
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AB and AC AC and AD |
AB and CB AC and CD |
Then, by definition of similar triangles, the lengths of corresponding sides are proportional.
△ABC∼△ACD | △ABC∼△CBD |
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ADAC=ACAB | DBCB=CBAB |
Note that for any two pairs of corresponding sides a similar proportion can be obtained. Now, applying the Properties of Equality, the proportion can be rewritten without fractions.