Isosceles Trapezoid
For all of the following problems, take as given (or constructed) an isosceles trapezoid with parallel sides of length a and b.
In terms of a and b, what is the length of a parallel line segment through the midpoints of the slant sides of the isosceles trapezoid?
In terms of a and b, what is the length of a parallel line segment through the intersection of the diagonals of the isosceles trapezoid?
In terms of a and b, what is the length of a parallel line segment that divides the isosceles trapezoid into two similar isosceles trapezoids?
In terms of a and b, what is the length of a parallel line segment that divides the isosceles trapezoid into two isosceles trapezoids of equal area?
Compare the four line segments on the same isosceles trapezoid. Are they always in the same relative position? Compare the four formulas. What inequalities will always hold? If it is useful to you, a GSP sketch is available by clicking here.

Related External Resources 
Investigating Properties
In this activity, we'll construct a demonstration sketch which could be used by middle school students to investigate the properties of quadrilaterals.
Geoboards in the classroom
This unit deals with the length and area of twodimensional geometric figures using the geoboard as a pedagogical device.
Submit your idea for an investigation to InterMath.
