A parallelogram whose four angles are all right angles (90°) is called a rectangle.
Properties of Rectangles
- All four angles are 90°.
- Opposite sides are equal and parallel (inherited from the properties of parallelograms).
- The diagonals are equal in length (AC=BD).
Example ①
In rectangle ABCD, when AC=10cm, find BD.
Solution: The diagonals of a rectangle are equal, so BD = AC = 10 cm
In rectangle ABCD, when AC=10cm, find BD.
Solution: The diagonals of a rectangle are equal, so BD = AC = 10 cm
Key Point
- Rectangle ⇒ Properties of parallelograms + equal diagonals
- Four angles are 90° ⇔ rectangle
Practice Problem
- Prove using congruence that the diagonals of a rectangle are equal (show that △ABC ≅ △BAD).
Answer and Explanation
- Answer: In △ABC and △BAD / ∠ABC=∠BAD=90° (rectangle) / AB=BA (common side) / BC=AD (opposite sides of a rectangle) / △ABC≅△BAD by SAS. Therefore, AC=BD.