Triangle ABC has a right angle at angle 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.
Below is the diagram representing the described triangle.
Can you please provide a step-by-step solution?
Also, it would be helpful if you could solve this without trignometry, because that is too complex for someone with my understanding of geometry. I think that you prove similarity by SSS, SAS, or AA, but I am not sure.
Thank you for your help!
+26397 Triangle ABC has a right angle at angle 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.
Below is the diagram representing the described triangle.
Geometric mean theorem:
(1)AB2=EB⋅BC(2)BC2=AB⋅BD(1)⋅(2):AB2⋅BC2=EB⋅BC⋅AB⋅BD|:(AB⋅BC)AB⋅BC=EB⋅BD
+26397 Triangle ABC has a right angle at angle 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.
Below is the diagram representing the described triangle.
Geometric mean theorem:
(1)AB2=EB⋅BC(2)BC2=AB⋅BD(1)⋅(2):AB2⋅BC2=EB⋅BC⋅AB⋅BD|:(AB⋅BC)AB⋅BC=EB⋅BD
