Quadrilaterals

Question 1

What is a quadrilateral?

Answer 1

A four-sided polygon

Question 2

What is a polygon?

Answer 2

A 2D figure with three or more sides

Question 3

What is a property that all quadrilaterals have?

Answer 3

The interior angles add up to 360°

Question 4

What is a trapezium?

Answer 4

A quadrilateral in which one pair of opposite sides are parallel

Question 5

What is a kite?

Answer 5

A quadrilateral in which two pairs of adjacent sides are equal

Question 6

What are the properties of a kite in terms of the diagonals?

Answer 6

The longer diagonal bisects the shorter diagonal
The longer diagonal bisects the angles that it runs through
The diagonals of a kite are perpendicular

Question 7

What is another property of a kite, concerning the angles?

Answer 7

One pair of opposite angles are equal

Question 8

What is a parallelogram?

Answer 8

A quadrilateral in which both pairs of opposite sides are parallel

Question 9

What are the properties of a parallelogram, concerning the sides?

Answer 9

Opposite sides are equal

Question 10

What are the properties of a parallelogram, concerning the angles?

Answer 10

Opposite angles are equal

Question 11

What are the properties of a parallelogram, concerning the diagonals?

Answer 11

The diagonals bisect each other

Question 12

What is a rhombus?

Answer 12

A parallelogram in which all the sides are equal

Question 13

What are the properties of a rhombus, concerning the diagonals?

Answer 13

The diagonals bisect each other at right angles

The diagonals bisect the angles that they run through

Question 14

What is a rectangle?

Answer 14

A parallelogram in which all corners are equal to 90°

Question 15

What are the properties of a rectangle, concerning the diagonals?

Answer 15

All of the diagonals are equal

Question 16

What is a square?

Answer 16

A rhombus in which all angles are equal to 90°

A rectangle in which all sides are equal

Question 17

How do you prove that something is a trapezium?

Answer 17

Prove that one pair of opposite sides are parallel

Question 18

How do you prove that something is a kite?

Answer 18

Two pairs of adjacent sides are equal

Question 19

How do you prove that something is a parallelogram?

Answer 19

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

Question 20

How do you prove that something is a rectangle?

Answer 20

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

Question 21

How do you prove that something is a rhombus?

Answer 21

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

Question 22

How do you prove that something is a square?

Answer 22

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