Draw two isosceles triangles, ∆abc and ∆adc with common base ac . vertexes b and d are in the opposite semi-planes determined by ac . draw the line segment bd . prove: ac ⊥ bd

Statement                                               Reason

∆ABC and ∆ADC are isosceles              Given

Segment AC is a common base
to ∆ABC and ∆ADC                                Given

Let K be the midpoint of the base
of segment AC, then BK is the
perpendicular bisector of segment         perpendicular bisector of isosceles AC.                                                         triangle property.

Also, DK is the perpendicular
bisector of segment AC.                        perpendicular bisector of isosceles                                                                    triangle property.

The length of what is left would be 1 1/2 feet long.