Test
Symmetry and transformations
Dynamic tasks about lines of symmetry, reflection, central symmetry, rotation and translation. The test develops the ability to recognise and apply geometric transformations.
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Sample questions
- How many lines of symmetry does the shown shape have?
- Which transformation is shown?
- Point A is reflected in the vertical line x = 5. What are the coordinates of the reflected point?
- Point A(___; ___) is reflected in the centre O(5; 5). What are the coordinates of the new point?
- Which direction will the arrow point after a ___° clockwise rotation?___
Symmetry and geometric transformations
A shape has line symmetry if it can be folded along a line so that both parts coincide. When a point is reflected across a line of symmetry, its perpendicular distance from the line remains equal on both sides.
Types of transformation
- A reflection flips a shape across a mirror line.
- A translation moves every point in the same direction and by the same distance.
- A rotation turns a shape around a centre through a stated angle.
- Central symmetry is equivalent to a 180° rotation.
These transformations preserve side lengths, angles and area. Only position or orientation changes. In coordinate tasks, verify the movement of every vertex separately.
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An angle is a geometric figure formed by two rays or straight lines that share a common endpoint, called the vertex, but extend in different directions. Angles are typically measured in degrees (°), but they can also be expressed in other units such as radians or gradians. Angles can vary in size and shape depending on the degree of their opening and other geometric properties. For example, a right angle has an opening of 90 degrees, while a straight angle has an opening of 180 degrees. Angles are a fundamental concept used in mathematics and various other fields where geometry is applied.
