Defining a Rectangle
Defining a Rectangle is a Grade 5 math skill from Illustrative Mathematics Chapter 7 (Shapes on the Coordinate Plane) that establishes a rectangle as a parallelogram with four right angles, all measuring 90°. Because a rectangle is a specific type of parallelogram, it inherits properties like opposite sides being parallel and equal in length. All squares are special rectangles where all four sides are also equal.
Key Concepts
Property A rectangle is a parallelogram with four right angles. All angles in a rectangle are congruent and measure $90^\circ$.
Examples A quadrilateral with vertices at $(0, 0)$, $(5, 0)$, $(5, 3)$, and $(0, 3)$ is a rectangle. If a parallelogram has one right angle, it must be a rectangle because its other properties force all other angles to be $90^\circ$. All squares are special types of rectangles.
Explanation A rectangle is a specific type of parallelogram, which means it inherits all the properties of a parallelogram, such as having opposite sides that are parallel and equal in length. The defining characteristic that distinguishes a rectangle from other parallelograms is that all four of its interior angles are right angles ($90^\circ$). This places rectangles as a sub category of parallelograms within the hierarchy of quadrilaterals.
Common Questions
What is the definition of a rectangle?
A rectangle is a parallelogram with four right angles, all measuring 90°. It has opposite sides that are parallel and equal in length. All squares are rectangles, but not all rectangles are squares.
How is a rectangle different from other parallelograms?
A rectangle is specifically a parallelogram where all four interior angles are exactly 90°. Other parallelograms (like rhombuses) may have equal sides but do not require right angles.
What chapter defines rectangles in Illustrative Mathematics Grade 5?
Defining a Rectangle is covered in Chapter 7 of Illustrative Mathematics Grade 5, titled Shapes on the Coordinate Plane.
Is every square a rectangle?
Yes. A square has four right angles (90°) and is therefore a type of parallelogram with four right angles, which makes it a rectangle. However, a rectangle is only a square if all four sides are also equal in length.
How do you identify a rectangle on a coordinate plane?
Plot the four vertices and verify that all four interior angles are right angles (90°). You can confirm right angles by checking that adjacent sides are perpendicular, meaning their slopes multiply to -1.