What is "in parallelogram pqsr?

Parallelogram PQSR

A parallelogram PQSR is a quadrilateral with two pairs of parallel sides. In this specific case, side PQ is parallel to side SR, and side PS is parallel to side QR.

Key properties include:

• Opposite Sides: Opposite sides are equal in length (PQ = SR and PS = QR).

• Opposite Angles: Opposite angles are equal in measure (∠P = ∠R and ∠Q = ∠S).

• Consecutive Angles: Consecutive angles (angles that share a side) are supplementary, meaning they add up to 180 degrees (e.g., ∠P + ∠Q = 180°).

• Diagonals: The diagonals of a parallelogram bisect each other. That is, they intersect at their midpoints. If the intersection point is M, then PM = MR and QM = MS. The diagonals, PR and QS, are generally not equal in length unless the parallelogram is a rectangle or a square.

• Area: The area of parallelogram PQSR can be calculated using the formula: Area = base × height. The "base" can be any side (e.g., PQ), and the "height" is the perpendicular distance from that base to the opposite side (SR). Alternatively, the area can be calculated using the lengths of two adjacent sides (e.g., PQ and PS) and the sine of the angle between them: Area = PQ × PS × sin(∠P).