Properties of Plane Shapes

Triangles: 

The triangle is shape that is formed by 3 straight lines that are called sides.

There are different ways of classifying triangles according to their sides or angles.

Triangles According to their Angles: 

1. Right Angle: The largest of the 3 angles is a right angle

2. Acute Angle: The largest of the 3 angles is an acute angle (less than 90 degrees).

In the example below the largest angle is 70º which is less than 90º

3. Obtuse Angle: The largest of the 3 angles is an obtuse angle (greater than 90º).

In the example below the largest angle is 135º which is greater than 90º

Triangles According to their Sizes:

1. Equilateral Triangle:

• All 3 sides are the same length.

• All three angles are congruent and are equal to 60 degrees.

2. Isosceles Triangle:

• It has 2 sides that are of equal length. (An Equilateral triangle is also isosceles. The definition of an equilateral triangle is that all three sides are of equal length; therefore any two sides are of equal length; and, therefore an equilateral triangle is isosceles).

• Angles opposite to these equal sides are also equal (so \( \scriptsize \angle x = \angle y \))

3. Scalene Triangle: A triangle which has all the sides and angles, unequal.

\( \scriptsize x \neq y \neq z \)

Quadrilaterals:

A quadrilateral is a four-sided 2D figure whose sum of internal angles is 360°.

There are two properties of quadrilaterals:

• A quadrilateral should be closed shape with 4 sides.
• All the internal angles of a quadrilateral sum up to 360°

There are 5 Types of Quadrilaterals which we will discuss below;

• Rectangle

• Square

• Trapezium

• Rhombus

• Parallelogram

The Rectangle

• The rectangle is a shape that has 4 sides.

• The distinguishing characteristic of a rectangle is that all 4 angles are equal to 90 degrees.

• Opposite sides of a rectangle are equal and Parallel

• Diagonals of a rectangle bisectBisect means dividing into two equal parts. It means to divide a geometric figure such as a line, an angle or any other shape into two congruent parts (or two parts that have the same shape and size). Point M bisects the segment. Since point M divides the segment into two parts that have the same size and shape, the segment is bisected. Since ray AB divides the angle into two parts that have the same size and shape, the... each other (Diagonals are equal)

The Square

• The square is a type of rectangle, but also a type of rhombus. It has characteristics of both of these.

• That is to say, all 4 angles are right angles, and all 4 sides are equal in length.

 The Trapezium 

• The sum of all the four angles of the trapezium is equal to 360°

• A trapezium has two parallel sides and two non-parallel sides.

• The diagonals of regular trapezium bisect each other.

The Rhombus:

• The rhombus is a shape formed by 4 straight lines.

• All sides are equal and, opposite sides are parallel to each other

• Unlike the rectangle, none of all 4 angles are equal to 90º.

The Parallelogram 

The parallelogram has the following properties:

• the opposite sides are parallel

• the opposite sides are congruent

• the diagonals bisect each other at the centre

The Circle

• Circle is perfect round shape.

• Circumference is the boundary of a circle.

• Arc is part of the circumference of a circle.

• Radius (plural radii) is a straight line from the centre to the circumference of a circle

• Diameter is any chord through the centre of a circle.

• Sector is the region between two radii and the circumference.

• Semi-circle is the region between a diameter and the circumference.