Question

move vertex d and observe how the measures change. make a conjecture. which of the following statements appear to be true? check all that apply. ac and bd are always equal. ae and ce are always equal. be and de are always equal. ac and bd always bisect each other ac and bd are always perpendicular. ae = 40 units ce = 40 units be = 32 units de = 32 units

Explanation:

In a parallelogram (the figure appears to be a parallelogram - though not explicitly stated, based on the properties being tested), the diagonals bisect each other. That means the mid - points of the diagonals divide them into equal segments. So, $AE = CE$ and $BE=DE$, and the diagonals $AC$ and $BD$ bisect each other. The diagonals of a general parallelogram are not equal in length and not perpendicular.

Answer:

AE and CE are always equal.
BE and DE are always equal.
AC and BD always bisect each other.