Revision:Shapes

TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Shapes

Triangles

Triangles are polygons with 3 sides. The angles in a triangle add up to 180 degrees.

Isosceles triangles have two equal angles. The sides of the triangle opposite the equal angles are equal in length to one another.

Equilateral triangles have all of their sides and angles equal. Since there are 180 degrees in a triangle and all the angles are equal, each angle is 60 degrees.

Scalene triangles

Right-angled triangles

Quadrilaterals

Quadrilaterals are polygons with 4 sides. The angles in any quadrilateral ad up to 360 degrees.

In a parallelograms opposite sides are parallel, opposite angles are equal, the diagonals bisect one another.

A rhombus is a parallelogram in which all four sides of equal length and in which the diagonals bisect one another at right angles. This gives the shape two lines of symmetry and rotational symmetry of order 2.

A trapezium has one pair of opposite sides which are parallel.

In a square all sides are equal in length, all interior angles are 90 degrees and the diagonals bisect one another at 90 degrees. This means opposite sides are parallel, there are 4 lines of symmetry and it has rotational symmetry order 4.

In a rectangle all angles are 90 degrees and diagonals bisect one another. Opposite sides are equal in length and parallel and there are two lines of symmetry.

A kite has two pars of adjacent sides of equal length. This means two of the angles are equal an the shape has one line of symmetry. A kite can either be a concave kite or a convex kite.....

Some quadrilateral classification questions

• Is a square always a rectangle?
• Is a rectangle always a square?
• Is a rectangle always a parallelogram?
• Is a parallelogram always a rectangle?
• Is a square always a rhombus?
• Is a rhombus always a square?
• Is a parallelogram always a rhombus?
• Is a rhombus always a parallelogram?
• Is a kite always a square?
• Is a rectangle always a kite?
• Is a square always a kite?
• Is a rectangle always a trapezium?
• Is a rhombus always a trapezium?
• Is a trapezium always a kite?

Look at the properties of each quadrilateral to decide if any of the questions can be answered 'YES'. What reasons are there for answering 'YES' or 'NO'. For those which answer 'NO' what extra properties would the shape need for the answer to be 'YES'?

Polygons

The word polygon means a many sided shape. They are all 'flat'(2-dimensional).

The simplest polygon is a triangle with three sides. Then we have a quadrilateral with 4 sides.

• Triangle - 3 sides
• Quadrilateral - 4 sides
• Pentagon - 5 sides
• Hexagon - 6 sides
• Heptagon - 7 sides
• Octagon - 8 sides
• Nonagon - 9 sides
• Decagon - 10 sides
• Hen-decagon - 11 sides
• Do-decagon - 12 sides

Comments

Need to add diagrams to illustrate most or all of these points.

Mention concave and convex kites.

A stuff about scalene triangles, right-angled triangles etc....