Two tests for a rectangle
Check the corners and check the sides.
What makes a rectangle?
A quadrilateral is a shape with four sides. A rectangle is one special kind of quadrilateral.
To decide whether a quadrilateral is a rectangle, what would you check?
What this lesson covers
The idea
A rectangle is a quadrilateral whose angles are all right angles (90°) and whose opposite sides are of equal length.
What makes a rectangle?
A quadrilateral is a shape with four sides. A rectangle is one special kind of quadrilateral.
To decide whether a quadrilateral is a rectangle, what would you check?
- Only its corners
- Only its sides
- Its corners and its sides
The test bench
Tap a shape. Run the corner test and the side test: tap each one to measure. Then decide.
Both tests must pass
A rectangle is a quadrilateral whose angles are all right angles (90°) and whose opposite sides are of equal length.
The leaning shape passed the side test but failed the corner test. A rectangle must pass both.
Notes
A rectangle is a quadrilateral whose angles are all right angles (90°) and whose opposite sides are of equal length.
Check yourself
PQRS has opposite sides of 7 cm and 3 cm, and angles of 80° and 100°. Is it a rectangle?
A rectangle has two neighbouring sides of 8 cm and 5 cm. How long is the side opposite the 8 cm side?
Answer: 8 cm
Opposite sides of a rectangle are equal, so the side opposite the 8 cm side is also 8 cm.
Which quadrilateral passes both tests, so it is a rectangle?
A rectangle has neighbouring sides of 9 cm and 5 cm. What is the sum of the lengths of all four sides?
Answer: 28 cm
The sides are 9, 5, 9 and 5 because opposite sides are equal. 9 + 5 + 9 + 5 = 28 cm.
- Yes, its opposite sides are equal. The side test passes, but a rectangle needs the corner test too. The angles are 80° and 100°, not 90°.
- No, its angles are not all 90° — correct. Yes! It fails the corner test, so it is not a rectangle.
- Yes, because it has four sides. Every quadrilateral has four sides. A rectangle must also pass the corner and side tests.
- Angles 70°, 110°, 70°, 110°; opposite sides equal. Opposite sides are equal, but the angles are not 90°. It fails the corner test.
- Sides 5, 5, 5, 5; angles 60°, 120°, 60°, 120°. The sides are equal, so opposite sides are equal, but the angles are not 90°.
- Angles 90°, 90°, 90°, 90°; opposite sides 6 cm and 6 cm, 4 cm and 4 cm — correct. Yes! All angles are 90° and opposite sides are equal.
- Angles 90°, 90°, 60°, 120°; sides 7, 4, 3, 4. Only two angles are 90°, and the opposite sides are not equal.