As shown in the figure, e is the outer point of parallelogram ABCD, and ab ⊥ EC, be ⊥ ed, is parallelogram ABCD a rectangle?

As shown in the figure, e is the outer point of parallelogram ABCD, and ab ⊥ EC, be ⊥ ed, is parallelogram ABCD a rectangle?

A parallelogram ABCD is not necessarily a rectangle
For example, the following method is an example:
1. Make a parallelogram ABCD so that ∠ a ＞ 90 degrees
2. Make a straight line FC ⊥ ab
3. Take BD as the diameter to make a circle, and the intersection line FC is at E
Then e must be outside the parallelogram ABCD, and ab ⊥ EC, be ⊥ ed
The parallelogram ABCD is not a rectangle

As shown in the figure, in the parallelogram ABCD, the point E is on the extension line of AB, and EC ‖ BD, we prove that be = ab

It is proved that ∵ ABCD is a parallelogram, ∵ ab ∥ CD, i.e. be ∥ CD, and ∵ EC ∥ BD, ∵ quadrilateral becd is a parallelogram. ∵ be = CD. ∵ be = ab

ABCD is a parallelogram, ad = a, de intersects the extension of AC at F, intersects be and E, DF = EF
Verification: AF is parallel to be
If AC = 2cf, ∠ ADC = 60 °, find the length of be

Let the intersection of AC and BD be o. since ABCD is a parallelogram, so do = ob, and because DF = Fe, angle ODF = angle BDE, so triangle ODF is similar to triangle BDE, so angle DOF = DBE, we can prove that AF is parallel to be