Properties of Parallelograms
Properties of Parallelograms covers the defining geometric properties: opposite sides are parallel and congruent, opposite angles are equal, and consecutive angles are supplementary (sum to 180°). Covered in Illustrative Mathematics Grade 6, Unit 1: Area and Surface Area, these properties help Grade 6 students identify and classify parallelograms and understand why the area formula A = base × height works. Recognizing these properties is foundational for geometry and area reasoning.
Key Concepts
A parallelogram is a quadrilateral with two pairs of opposite sides that are parallel, which gives it the following properties: Opposite sides are congruent (equal in length). Opposite angles are congruent (equal in measure). Consecutive angles are supplementary (their sum is $180^\circ$). The diagonals bisect each other (they cut each other into two equal halves).
Common Questions
What are the properties of a parallelogram?
A parallelogram has two pairs of parallel sides, opposite sides that are congruent, opposite angles that are equal, and consecutive angles that are supplementary (add to 180°).
Is a rectangle a parallelogram?
Yes. A rectangle is a special parallelogram where all four angles are 90°. Squares and rhombuses are also special parallelograms.
What does it mean for opposite sides to be congruent in a parallelogram?
The two longer sides are equal in length and the two shorter sides are equal in length. The sides opposite each other are identical.
Where are properties of parallelograms in Illustrative Mathematics Grade 6?
This topic is in Unit 1: Area and Surface Area of Illustrative Mathematics Grade 6.
How do parallelogram properties help find area?
Knowing the base and the perpendicular height (not the slant side), you can apply A = b × h. The parallel sides ensure the height is constant across the full base.