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: Recall properties of parallelogram

In a parallelogram, the diagonals bisect each other. That is, the point of intersection of the diagonals divides each diagonal into two equal - length segments.

Step2: Analyze each statement

1. For a general parallelogram, the diagonals \(AC\) and \(BD\) are not always equal. Rectangles are the special case where diagonals are equal.
2. Since the diagonals of a parallelogram bisect each other, \(AE = CE\) always holds.
3. Since the diagonals of a parallelogram bisect each other, \(BE=DE\) always holds.
4. The diagonals of a parallelogram always bisect each other, so \(\overline{AC}\) and \(\overline{BD}\) always bisect each other.
5. For a general parallelogram, the diagonals are not always perpendicular. Rhombuses are the special case where diagonals are perpendicular.

Answer:

AE and CE are always equal.
BE and DE are always equal.
\(\overline{AC}\) and \(\overline{BD}\) always bisect each other.