PROBLEMS: Isosceles trapezoid
For
all of the following problems, take as given (or constructed)
an isosceles trapezoid with parallel sides of length a and b.
What is the length, in terms of a and b,
of a parallel line segment through the midpoints of the slant
sides of the isosceles trapezoid?
What is the length, in terms of a and b,
of a parallel line segment through the intersection of the
diagonals of the isosceles trapezoid?
Suggestions and Discussion
What is the length, in terms of a and b,
of a parallel line segment that divides the isosceles trapezoid
into two similar isosceles trapezoids?
What is the length, in terms of a and b,
of a parallel line segment that divides the isosceles trapezoid
into two isosceles trapezoids of equal area?
Compare the four line segements 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
.
Use ruler and compass contructions, or use Geometer's sketchpad,
to construct the line segment parallel to the bases of
length a and b to divide the isosceles trapezoid
into two similar trapezoids.
Use ruler and compass contructions, or use Geometer's sketchpad,
to construct the line segment parallel to the bases of
length a and b to divide the isosceles trapezoid
into two trapezoids having the same area.
Consider your definition of an isosceles trapezoid. Is a
rectangle an isosceles trapezoid? In this problem, what is the
condition in the inequalities when a = b ? Does
your definition of an isosceles trapezoid allow you to demonstrate that point?
Return to EMAT
4600/6600 Page