Lesson 4, Topic 1
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# Properties of Plane Shapes

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## 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.

$$\scriptsize x \neq y \neq z$$

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 bisect 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