Triangle ABC has a right angle at B. Legs AB and CB are extended past point B to points D and E, respectively, such that angle EAC = angle ACD = 90 degrees. Prove that EB * BD = AB * BC.

Guest Jan 27, 2019

#1**+1 **

A

E B C

D

Angle AEB = Angle BAC

Angle ABE = Angle ABC

Thus, by AA congruency, triangle EBA is similar to triangle ABC

Angle CAB = Angle BCD

Angle CBA = Angle CBD

Again, by AA congruency, triangle ABC is similar to triangle CBD

So..by transivity......triangle EBA is similar to triangle CBD

So

EB / BA = CB / BD

So

EB * BD = BA * CB which is the same as.....

EB * BD = AB * BC

CPhill Jan 27, 2019