Imagine [math]\triangle ABC[/math] is fixed. Point [math]D[/math] lies on a line through [math]C[/math] parallel to segment [math]AB[/math]. Segments [math]EF[/math] and [math]GH[/math] lie on a line parallel to segment [math]AB[/math]. [br][br]Explain why [math]GH=EF[/math] for any position of [math]D[/math] on that line and for any position of [math]E[/math] on segment [math]AC[/math]. [br][br]What if you begin with a different [math]\triangle ABC[/math]?
Explain why [math]GH=EF[/math] for any position of [math]D[/math] on that line and for any position of [math]E[/math] on segment [math]AC[/math].
By various similar triangles, [math]\frac{GH}{AB}=\frac{DH}{DB}=\frac{DJ}{DK}=\frac{CE}{CA}=\frac{EF}{AB}[/math]. So [math]GH=EF[/math].