1, define the method
A parallelogram with right angles is a rectangle. Prove: According to the properties of parallelogram, we know that the diagonals of parallelogram are equal and the opposite sides are parallel.
Therefore, if an angle is a right-angled parallelogram, then one side of the angle is perpendicular to the extension line of the other side, forming a right-angled triangle. According to the nature of right triangle, we know that the center line of hypotenuse of right triangle is equal to half of hypotenuse. Therefore, the diagonals of parallelograms are equal and bisected each other, thus forming a rectangle.
2. Theorem method
A quadrilateral with three angles at right angles is a rectangle. It is proved that if any quadrilateral has three right angles, then the fourth angle is also a right angle. This is because in any quadrilateral, the sum of two diagonal angles is always 180 degrees, and three right angles have occupied 180 degrees, so the fourth angle is also a right angle. Therefore, a quadrilateral is a rectangle.
3. Parallel line method
If a diagonal line is perpendicular to two parallel opposite sides, then a quadrilateral is a rectangle. It is proved that let this quadrilateral be ABCD, where AC is diagonal and AB and BC are two parallel opposite sides. Since AC is perpendicular to AB and AC is perpendicular to BC, AC is perpendicular to AB and BC.
According to the properties of parallelogram, we know that the diagonal of parallelogram is equal. So the midpoint m of AC is also the midpoint of BD, so BD is also perpendicular to AC. Therefore, a quadrilateral is a rectangle.
Application of rectangle
Rectangles are widely used in daily life. For example, in architecture, rectangle is a common shape, which can be used for the design and construction of doors, windows, walls and floors. In electronic equipment, rectangular screen and keyboard are one of the most common input and output devices; In transportation, rectangular containers are widely used in cargo transportation.
In addition, rectangles are widely used in mathematics, physics, chemistry and other fields.