In the triangle ABC, the angles C = 90 °, D and E are the points on AB and AC respectively. Ad times AB = AE times AC, it is proved that ED is perpendicular to ab C: [documents and settings] administrator [desktop] unnamed.jpg

In the triangle ABC, the angles C = 90 °, D and E are the points on AB and AC respectively. Ad times AB = AE times AC, it is proved that ED is perpendicular to ab C: [documents and settings] administrator [desktop] unnamed.jpg

Ad times AB = AE times AC
Ad / AC = AE / AB angle a is the common angle
Then the triangle ade is similar to the triangle ACB
∠ ade = ∠ C = 90 degrees
That is, ED is perpendicular to ab