2.1 Similarity and Enlargement

• Similar figures and their properties
• Scale factor
• Enlargement: centre of enlargement and scale factor
• Negative and fractional scale factors
• Applications of similarity in real life

• identify similar figures and state their properties
• determine the scale factor between similar figures
• construct enlargements given a centre and a scale factor
• apply similarity to solve problems involving heights and distances
• appreciate the use of similarity in maps, models and design

“How can you measure something too tall to reach?”

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1. Similar figures and scale factor
   40 min · 2 practice tasks · quiz
   What makes two shapes similar, and how to use that to measure the unreachable.
2. Enlargement
   40 min · 2 practice tasks · quiz
   Producing a similar figure from a centre, including fractional and negative factors.
3. Corresponding parts and AA similarity
   40 min · 1 practice tasks · quiz
   Name similar triangles in matching order, then prove them similar with two equal angles.
4. Missing lengths by proportion
   40 min · 1 practice tasks · quiz
   Set up one pair of corresponding sides as a scale factor, then find every other length.
5. Nested triangles and parallel lines
   40 min · 1 practice tasks · quiz
   A line parallel to one side of a triangle cuts off a smaller triangle similar to the whole.
6. Scale factor in both directions
   40 min · 1 practice tasks · quiz
   k from object to image is the reciprocal of k from image to object.
7. Area scale factor
   40 min · 1 practice tasks · quiz
   If lengths multiply by k, areas multiply by k squared.
8. Volume scale factor and models
   40 min · 1 practice tasks · quiz
   If lengths multiply by k, volumes multiply by k cubed. That is how models and tanks scale.
9. Enlargement not from the origin
   40 min · 1 practice tasks · quiz
   Subtract the centre, multiply by k, add the centre back. Rays still run through the centre.
10. Negative scale factors on the grid
    40 min · 1 practice tasks · quiz
    A negative k still multiplies distances by |k|, but the image sits on the other side of the centre, inverted.
11. Finding the centre of enlargement
    40 min · 1 practice tasks · quiz
    Join each vertex to its image; the rays meet at the centre. Then read k from distances along one ray.
12. Maps, models and inaccessible distances
    40 min · 1 practice tasks · quiz
    Read a map scale, and measure a tree or a river you cannot walk across, using similar triangles.