Understanding the Properties of Parallelograms: Theorems and Examples

Feb 07, 2026

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This section explores the key properties of parallelograms, a type of quadrilateral where opposite sides are parallel. We introduce important theorems: opposite sides are congruent, opposite angles are congruent, consecutive angles are supplementary, and the diagonals bisect each other. To illustrate these properties, we provide an example involving quadrilateral PQRS, demonstrating how to find side lengths and angle measures based on given values. Understanding these foundational principles is essential for geometry studies.

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Understanding the Properties of Parallelograms: Theorems and Examples

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Section 6.3 Properties of Parallelograms
Parallelogram Quadrilateral whose opposite sides are parallel So ABCD is a parallelogram ABCD AB and DC are parallel AD and BC are parallel
Properties of Parallelograms Thm 6.3: If a quadrilateral is a parallelogram, then its opposite sides are congruent. Thm 6.4: If a quadrilateral is a parallelogram, then its opposite angles are congruent. Thm 6.5: If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. Thm 6.6: If a quadrilateral is a parallelogram, then its diagonals bisect each other.
Exs: 1. You have PQRS. Find SR, ST, m<PQR and m<QRS if m< <QPS = 70° SR= 5(opposite sides congruent) ST= QT= 3(diagonal PR bisects diagonal QS) m<PQR= 110° (consect angles supple) M<QRS = 70 °(opp angles are congruent)