Rectangles
Overview
A rectangle is a parallelogram with two added properties: four right angles and diagonals that are congruent. It inherits all five parallelogram properties, so its diagonals bisect each other as well — and because the diagonals are both congruent and bisecting, they cut the rectangle into four isosceles triangles. This lesson uses those facts to find angle measures and lengths.
Vocabulary
- Rectangle
- A parallelogram with four right angles. The diagonals of a rectangle are congruent.
- Parallelogram
- A quadrilateral with both pairs of opposite sides parallel.
- Right Angle
- An angle whose measure is 90°.
- Isosceles Triangle
- A triangle with at least two congruent sides. The four triangles formed by the diagonals of a rectangle are all isosceles.
Main Ideas
- A rectangle has all five properties of a parallelogram: opposite sides parallel and congruent, opposite angles congruent, consecutive angles supplementary, and diagonals that bisect each other.
- A rectangle has four right angles.
- The diagonals of a rectangle are congruent — this is the added property that separates rectangles from other parallelograms.
- Because the diagonals are congruent and bisect each other, all four half-diagonals are the same length, forming four isosceles triangles.
- A diagonal splits a right angle of the rectangle into two parts that add to 90°, and alternate interior angles formed with the parallel sides are congruent.
Lesson Notes
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Lesson Video
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Practice Problems
Want More Practice?
Download the practice worksheet for this lesson, work the problems, then check your work with the solutions.