Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Line Symmetry (2D): A shape has line symmetry if a line can be drawn dividing the shape into two identical halves that are mirror images of each other.
Rotational Symmetry (2D): A shape has rotational symmetry if it looks the same after some rotation of less than 360 degrees about its center. The 'Order' is the number of times it looks the same in one full turn.
Symmetry of Regular Polygons: For a regular polygon with 'n' sides, there are 'n' lines of symmetry and the order of rotational symmetry is 'n'.
Planes of Symmetry (3D): A flat surface that cuts a 3D object into two identical halves that are mirror images of each other.
Axis of Rotational Symmetry (3D): An imaginary line through a 3D object such that the object can be rotated around it and look unchanged multiple times in a full 360-degree rotation.
Symmetry in Quadrilaterals: Understanding specific properties (e.g., a Parallelogram has no lines of symmetry but has rotational symmetry of order 2; a Kite has 1 line of symmetry but rotational symmetry of order 1).
📐Formulae
💡Examples
Problem 1:
Determine the number of lines of symmetry and the order of rotational symmetry for a Rhombus.
Solution:
Lines of symmetry: 2; Order of rotational symmetry: 2.
Explanation:
A rhombus has two lines of symmetry, which are its diagonals. It looks identical twice during a 360-degree rotation (at 180 degrees and 360 degrees).
Problem 2:
How many planes of symmetry does a square-based pyramid (regular) have?
Solution:
4 planes of symmetry.
Explanation:
There are 2 planes that pass through the opposite vertices of the base and the apex, and 2 planes that pass through the midpoints of opposite base edges and the apex.
Problem 3:
A regular octagon is rotated about its center. What is the smallest angle of rotation that maps the octagon onto itself?
Solution:
Explanation:
Since a regular octagon has an order of rotational symmetry of 8, the smallest angle is calculated as .