Angles and Shapes, Symmetrical patterns Chapter Notes | Year 5 Mathematics IGCSE (Cambridge) - Class 5 PDF Download

Symmetrical Patterns

• Symmetry refers to a pattern or shape that can be divided into two or more identical parts.
• A symmetrical pattern may have multiple lines of symmetry, such as two or four, depending on how it is designed.
• Example: A completed symmetrical pattern can have two lines of symmetry, where reflecting across these lines produces identical halves.

Lines of symmetry can be:

• Horizontal: A line that runs left to right.
• Vertical: A line that runs up and down.
• Diagonal: A line that runs at an angle, neither horizontal nor vertical.

Identifying and Reasoning about Angles

An angle is formed by two rays or lines that share a common endpoint, measured in degrees.

Types of angles

• Acute angle: Less than a quarter turn (less than 90°).
• Right angle: Exactly a quarter turn (90°), marked with a square symbol.
• Obtuse angle: Greater than a right angle but less than a half turn (between 90° and 180°).
• Reflex angle: Greater than a half turn but less than a whole turn (between 180° and 360°).
• Half turn: Exactly 180°, equivalent to a straight line.
• Whole turn: Exactly 360°, a complete rotation.

The angle on a straight line is always 180°, equivalent to a half turn (clockwise or anticlockwise).
Calculating missing angles on a straight line:

• Example: If one angle is 60°, the missing angle is 180° - 60° = 120°.
• Example: If one angle is 145°, the missing angle is 180° - 145° = 35°.

Triangles

Triangles are classified by their side lengths:

• Scalene triangle: All three sides are of different lengths.
• Isosceles triangle: Two sides are of equal length.
• Equilateral triangle: All three sides are of equal length.

Markings are used to indicate equal side lengths:

• Equal sides are marked with identical symbols (e.g., a single hash mark or double hash mark).

Symmetry in triangles:

• Isosceles triangles have one line of symmetry, passing through the vertex between the equal sides and bisecting the base.
• Equilateral triangles have three lines of symmetry, each passing through a vertex and the midpoint of the opposite side.

Tessellation:

• ​Some triangles can tessellate, meaning they can cover a plane without gaps or overlaps.
• Equilateral triangles tessellate due to their equal sides and angles, fitting together perfectly.

Properties of isosceles triangles:

• Two sides are equal in length.
• The angles opposite the equal sides (base angles) are equal.

An isosceles triangle can have:

• Acute angles (all angles less than 90°).
• An obtuse angle (one angle greater than 90°).
• A right angle (one angle exactly 90°).