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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.

 Jan 27, 2019
 #1
avatar+111325 
+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

 

 

 

cool cool cool

 Jan 27, 2019
 #2
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+1

Thank you

Guest Jan 27, 2019

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