Isosceles Trapezoid Investigation

Kevin Tobe
A trapezoid is a quadrilateral with one set of parallel sides, called the bases. Base angles are consecutive angles whose common side is a base. For this exploration, the bases are purple.
Move the points until you get a trapezoid where the non-base sides are the same length. Trapezoids where the non-base sides are congruent are called isosceles trapezoids. What do you notice about the pairs of base angles in an isosceles trapezoid? Is there any relationship between the angles at opposite vertices within the isosceles trapezoid? Turn on the diagonals by using the check box. What can you say about the lengths of diagonals within an isosceles trapezoid? Is this true for the diagonals in a trapezoid that is not isosceles? Turn off the diagonals and turn on the midsegment. How does the length of the midsegment relate to the length of the bases?