rectangle

Rectangle.A quadrilateral whose four angles are equal, that is, whose 4 angles are equal to $90^{\\circ}$ .

Any rectangle is a parallelogram.
This follows from angles $\\angle BAD$ and $\\angle ADC$ adding up $180^{\\circ}$ .

Since parallelograms have their opposite sides equal, so do rectangles. In the picture, $AB=CD$ and $BC=DA$ .

Rectangles are the only parallelograms to be also cyclic (since opposite angles add up $180^{\\circ}$ .

Notice that every square is also a rectangle, but there are rectangles that are not squares

Rectangles have their two diagonals equal (since triangles $A B C$ and $A B D$ are congruent), A nice result following from this is that the quadrilateral obtained by joining the midpoints of the sides is a rhombus.

Since $P Q$ joins midpoints of sides in triangle $A B C$ , we have $PQ=CA/2$ . Similarly we have $RS=CA/2$ , $QR=BD/2$ and $SP=BD/2$ and thus the sides of quadrilateral $P Q R S$ are all equal, in other words, $P Q R S$ is a rhombus.

单词	Rectangle
释义	rectangle Rectangle.A quadrilateral whose four angles are equal, that is, whose 4 angles are equal to $90^{\\circ}$ . Any rectangle is a parallelogram. This follows from angles $\\angle BAD$ and $\\angle ADC$ adding up $180^{\\circ}$ . Since parallelograms have their opposite sides equal, so do rectangles. In the picture, $AB=CD$ and $BC=DA$ . Rectangles are the only parallelograms to be also cyclic (since opposite angles add up $180^{\\circ}$ . Notice that every square is also a rectangle, but there are rectangles that are not squares Rectangles have their two diagonals equal (since triangles $A B C$ and $A B D$ are congruent), A nice result following from this is that the quadrilateral obtained by joining the midpoints of the sides is a rhombus. Since $P Q$ joins midpoints of sides in triangle $A B C$ , we have $PQ=CA/2$ . Similarly we have $RS=CA/2$ , $QR=BD/2$ and $SP=BD/2$ and thus the sides of quadrilateral $P Q R S$ are all equal, in other words, $P Q R S$ is a rhombus.
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