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:

Step1: Analyze property of diagonals in general parallelogram

In a parallelogram, the diagonals bisect each other. That is, for parallelogram \(ABCD\) with diagonals \(AC\) and \(BD\) intersecting at \(E\), \(AE = CE\) and \(BE=DE\).

Step2: Check length - equality of diagonals

The diagonals of a parallelogram are not always equal. So \(AC\) and \(BD\) are not always equal.

Step3: Check perpendicular - property of diagonals

The diagonals of a general parallelogram are not always perpendicular.

Answer:

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