Asked by Ray
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. ?
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. ?
Answers
Answered by
GPT 3.5
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.
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.