Quadrilaterals Flashcards
What is a quadrilateral?
A four-sided polygon
What is a polygon?
A 2D figure with three or more sides
What is a property that all quadrilaterals have?
The interior angles add up to 360°
What is a trapezium?
A quadrilateral in which one pair of opposite sides are parallel
What is a kite?
A quadrilateral in which two pairs of adjacent sides are equal
What are the properties of a kite in terms of the diagonals?
The longer diagonal bisects the shorter diagonal
The longer diagonal bisects the angles that it runs through
The diagonals of a kite are perpendicular
What is another property of a kite, concerning the angles?
One pair of opposite angles are equal
What is a parallelogram?
A quadrilateral in which both pairs of opposite sides are parallel
What are the properties of a parallelogram, concerning the sides?
Opposite sides are equal
What are the properties of a parallelogram, concerning the angles?
Opposite angles are equal
What are the properties of a parallelogram, concerning the diagonals?
The diagonals bisect each other
What is a rhombus?
A parallelogram in which all the sides are equal
What are the properties of a rhombus, concerning the diagonals?
The diagonals bisect each other at right angles
The diagonals bisect the angles that they run through
What is a rectangle?
A parallelogram in which all corners are equal to 90°
What are the properties of a rectangle, concerning the diagonals?
All of the diagonals are equal
What is a square?
A rhombus in which all angles are equal to 90°
A rectangle in which all sides are equal
How do you prove that something is a trapezium?
Prove that one pair of opposite sides are parallel
How do you prove that something is a kite?
Two pairs of adjacent sides are equal
How do you prove that something is a parallelogram?
Prove one of the following:
Both pairs of opposite sides are equal
Both pairs of opposite sides are parallel
One pair of opposite sides are equal and parallel
Both pairs of opposite angles are equal
Diagonals bisect each other
How do you prove that something is a rectangle?
First prove that it is a parallelogram then:
Prove that one of the interior angles is 90°
Or that the diagonals are equal in length
How do you prove that something is a rhombus?
First prove that it is a parallelogram then:
Prove that a pair of adjacent sides are equal
Or prove that the diagonals bisect at right angles
How do you prove that something is a square?
Prove that it is a rectangle with adjacent sides equal
Or first prove that it is a rhombus then:
Prove that it has an interior right angle
Or prove that the diagonals are equal
