Parallelograms
Overview
A parallelogram is the workhorse of the quadrilateral family. This lesson starts with its definition — both pairs of opposite sides parallel — and builds the five properties that follow from it: opposite sides congruent, opposite angles congruent, consecutive angles supplementary, and diagonals that bisect each other. Because properties are inherited down the family tree, everything in this lesson will also be true for rectangles, rhombuses, and squares.
Vocabulary
- Quadrilateral
- A polygon with four sides.
- Parallelogram
- A quadrilateral with both pairs of opposite sides parallel.
- Opposite Sides / Opposite Angles
- Sides or angles of a quadrilateral that do not share a vertex or a side — they are across the figure from each other.
- Consecutive Angles
- Two angles of a quadrilateral that share a side. In a parallelogram, consecutive angles are supplementary (their measures add to 180°).
- Diagonal
- A segment that connects two non-consecutive vertices of a polygon. A quadrilateral has two diagonals.
Main Ideas
- In a parallelogram, both pairs of opposite sides are congruent.
- In a parallelogram, both pairs of opposite angles are congruent.
- In a parallelogram, consecutive angles are supplementary, because each side is a transversal intersecting parallel lines.
- The diagonals of a parallelogram bisect each other — each diagonal is cut into two congruent parts by the other.
- To name a polygon, start at one vertex and move around the figure in order, clockwise or counterclockwise. A quadrilateral ABCD has diagonals AC and BD.
- Properties are inherited as you move down the polygon family tree: every rectangle, rhombus, and square is a parallelogram first.
Lesson Notes
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Lesson Video
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Practice Problems
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Download the practice worksheet for this lesson, work the problems, then check your work with the solutions.