Question 407097
Just do some angle chasing:


{{{drawing(200, 200, -10, 10, -1, 10,


triangle(-9, 0, 9, 0, -5, sqrt(46)),
line(-5, sqrt(46), -5, 0),
locate(-9, 0, A)
locate(-5, sqrt(46), B),
locate(9, 0, C),
locate(-5, 0, D),
locate(-9, 1, alpha)

)
}}}

Letting angle BAD = alpha, it follows that angle ABD = 90 - alpha. Since angle ABC is right, angle CBD = alpha, and angle DCB = 90 - alpha. You can show by angle-angle-angle similarity that all three triangles are similar.