Question

Trying to figure out answer and trying to show proof on how to get answer

Answer 1

1. AB*BE=CB*BD

Reason:Given

2.

`(CB)/(BE)=(AB)/(BD)`

Reason:

This result comes from the statement 1 because by moving BE to the righ hand side and BD to the left hand side, we have the previous result. This property is also know as proportion of the corresponding sides.

3.

`\angle ABC\cong\angle DBE`

Reason: They are vertical opposite angles.

4.

`\Delta ABC\approx\Delta DBE`

Reason. SAS (side-angle-side) theorem.

This theorem states that if two side and the included angle are equal to the two sides and the included angle of another triangle, then the triangles are congruent.

where the congruent sides are colored in the same color. The blue angle measure the same in both triangles and it is the included angle between sides red and green.