Geometry-Quadrilaterals

Question 1

Parallelogram (definition)

Quadrilaterals

Answer 1

• opposite sides are equal
• opposite sides are parallel

Question 2

Rectangle (definition)

Quadrilaterals

Answer 2

• all angles are 90 degrees
• opposite sides are equal

A rectangle is also a parallelogram

Question 3

Square (definition)

Quadrilaterals

Answer 3

• all angles are 90 degrees
• all sides are equal

A square is also a rectangle, a rhombus, and a parallelogram

Question 4

Rhombus (definition)
also called a rhomb

Quadrilaterals

Answer 4

• all sides are equal
• opposite sides are parallel

Properties of a rhombus:
- its diagonals bisect each other at 90 degrees
- opposite angles are equal

A rhombus is also a parallelogram and it is also a kite.

Question 5

Kite (definition)

Quadrilaterals

Answer 5

Kite is a quadrilateral that has:
- 2 pairs of sides
- each pair consists of ADJACENT equal-length sides

Properties of a kite:
- the diagonals meet at 90 degrees
- only one diagonal bisects the other diagonal

A kite may or may not be a rhombus!

Question 6

Trapezium (UK definition)

Attention: in the US, Trapesium is called Trapezoid!
Quadrilaterals

Answer 6

Trapezium (UK definition):
- Trapezium is a quadrilateral that has only ONE pair of parallel sides
- Isosceles trapezium: two sides that are NOT parallel are equal

The area of ANY trapezium (isosceles or not) is equal to:

the average of 2 parallel sides x height
(derivation in the AoPS book)

Question 7

Trapezoid (UK definition)

Attention: in the US, Trapezoid is called Trapesium!
Quadrilaterals

Answer 7

Trapezoid (UK definition):

Trapezoid is a quadrilateral that has NO parallel sides