The two statements that are always true for any parallelogram are:

1. A diagonal of a parallelogram creates two congruent triangles.

   • This is always true because a diagonal divides the parallelogram into two triangles, which are congruent by SAS (Side-Angle-Side) Congruence Theorem since opposite sides are equal, and the included angle is the same.

2. Diagonals of a parallelogram bisect each other.

   • This is always true because in any parallelogram, the diagonals always cut each other into two equal halves, dividing each diagonal into two equal segments.

The incorrect statements:

• Adjacent angles of a parallelogram are congruent (False).

  • Adjacent angles are supplementary (sum to 180°), but they are not necessarily equal unless the parallelogram is a rectangle.

• All parallelograms are rectangles (False).

  • Some parallelograms are not rectangles (e.g., rhombuses that are not squares). Rectangles are a special type of parallelogram with right angles.

• Opposite angles of a parallelogram are supplementary (False).

  • Opposite angles are equal, not supplementary. They are only supplementary if the parallelogram is a rectangle (where each angle is 90°, making opposite angles sum to 180°).

Would you like a visual explanation or further clarification?

Related Questions:

1. What are the properties of a parallelogram?
2. How do you prove that diagonals of a parallelogram bisect each other?
3. Can a parallelogram have all four sides equal but not be a rectangle?
4. What makes a rectangle different from a parallelogram?
5. How do you use coordinate geometry to prove a quadrilateral is a parallelogram?

Tip: In a parallelogram, the sum of consecutive angles is always 180°, which helps in angle calculations.