## What statement would be sufficient to prove that a quadrilateral is a rhombus the quadrilateral has four congruent angles?

If all sides of a quadrilateral are congruent, then it’s a rhombus (reverse of the definition). If the diagonals of a quadrilateral bisect all the angles, then it’s a rhombus (converse of a property).

## Which of the following conditions are sufficient individually to guarantee that ABCD is a parallelogram?

If — AB ≅ — CD and — BC ≅ — DA , then ABCD is a parallelogram. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

**What are the rules for a parallelogram?**

There are six important properties of parallelograms to know:

- Opposite sides are congruent (AB = DC).
- Opposite angels are congruent (D = B).
- Consecutive angles are supplementary (A + D = 180°).
- If one angle is right, then all angles are right.
- The diagonals of a parallelogram bisect each other.

### What are four geometric attributes you know because ABCD is a parallelogram?

you know because ABCD is a parallelogram? are congruent (AB O CD, BC O DA) ; opposite angles are congruent (lA O lC, lB O lD); opposite sides are parallel (AB n CD, BC n DA); consecutive angles are supplementary (mlA 1 mlB 5 180, mlB 1 mlC 5 180, mlC 1 mlD 5 180, mlD 1 mlA 5 180);

### What would be the best method to prove a quadrilateral is a rhombus?

To prove a quadrilateral is a rhombus, here are three approaches: 1) Show that the shape is a parallelogram with equal length sides; 2) Show that the shape’s diagonals are each others’ perpendicular bisectors; or 3) Show that the shape’s diagonals bisect both pairs of opposite angles.

**What must M BCD be for ABCD to be a parallelogram?**

In order for ABCD to be a parallelogram, the diagonals must bisect each other. If segment AC bisects segment BD, then 4y – 5 = 2y + 1. Solving this equation, we get that y = 3. If segment BD bisects segment AC, then 4x = x + 3, so x = 1.

#### Are opposite sides of a parallelogram equal?

A parallelogram is a quadrilateral whose opposite sides are parallel. The opposite angles of a parallelogram are equal. The opposite sides of a parallelogram are equal.