given: AB*BE = CB*BD
prove: triangle ABC ~ triangle DBE
statements:
1. AB*BE = CB*BD
2. CB/BE = AB/BD
3. angle ABC ~= angle DBE
4. triangle ABC ~ triangle DBE
reasons:
1. given
2. property of ?
3. ?
4. ?
Reason for statement 2: CB/BE = AB/BD is the ratio of corresponding sides in the two triangles. This is a property of similar triangles.
Reason for statement 3: If two triangles have equal sides, then their corresponding angles are also equal. Therefore, if AB*BE = CB*BD, the corresponding angles ABC and DBE are congruent.
Reason for statement 4: From statement 3, we know that angle ABC ~= angle DBE and from statement 2, we know that the corresponding sides have the same ratio. Therefore, the two triangles satisfy the conditions of similarity and are therefore similar.