The nature of Zheng shape

The nature of Zheng shape

Zheng shape corresponds to the definition of rectangle. The definition of Zheng shape is that two groups of quadrilateral whose adjacent sides are equal are Zheng shape. The second definition of Zheng shape is that there is a diagonal line dividing vertically and the other quadrilateral is Zheng shape. Obviously, diamond is a special Zheng shape

The definition of Zheng shape
The definition should be accurate

The two groups of quadrilateral whose adjacent sides are equal are Zheng
Zhou En en

The character of angle and diagonal of Zheng shape

(1) Property 1: one set of diagonally equal, another set of diagonally unequal
Property 2: two diagonals are perpendicular to each other, only one of which is bisected by the other
(2) decision 1: only one diagonal bisection diagonal quadrilateral is Zheng shape
Decision 2: two diagonals are perpendicular to each other and only one quadrilateral is Zheng
Proof of decision 1:
It is known that in quadrilateral ABCD, diagonal AC bisects a and C, and diagonal BD bisects B and D
Verification: quadrilateral ABCD is Zheng shape
It is proved that ∵ BAC = DAC, ∵ BCA = DCA, AC = AC, ABC ≌? ADC (ASA)
　　∴AB=AD,CB=CD.
Easy to know AC ⊥ BD,
And ∵ abd ≠ CBD, ∵ BAC ≠ BCD. ∵ ab ≠ BC
The quadrilateral ABCD is a Zheng
Classification and induction, determination and properties of congruent triangles
[analysis] (1) it can also have the following properties:
Property 3: only one diagonal bisects the diagonal
Property 4: two sets of opposite sides are not parallel
(2) it can also be judged as follows:
Decision 3: in quadrilateral ABCD, AC ⊥ BD, ∠ B = ∠ D, ∠ a ≠ C, then quadrilateral ABCD is Zheng shape
Decision 4: in quadrilateral ABCD, if AB = ad, ∠ B = ∠ D, ∠ a ≠ C, then quadrilateral ABCD is Zheng shape
Decision 5: in quadrilateral ABCD, AC ⊥ BD, ab = ad, ∠ a ≠ C, then quadrilateral ABCD is Zheng shape

What is the definition of Zheng shape? What are its characteristics?

The definition of Zheng shape is: two groups of quadrilateral whose adjacent sides are equal are Zheng shape