4.3 Similarity and Enlargement

• Similar figures
• Properties of enlargement
• Linear scale factor

• identify similar figures and their properties
• draw similar figures in different situations
• determine properties of enlargement of different figures
• apply properties of enlargement to draw similar objects and their images
• determine the linear scale factor of similar figures
• promote the use of similarity and enlargement in real-life situations

“What are similar objects?”

“How do we use enlargement in real-life situations?”

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1. Similar figures
   40 min · 1 practice tasks · quiz
   Two figures are similar when they have the same shape, whatever their size.
2. The two tests for similarity
   40 min · 1 practice tasks · quiz
   Corresponding angles equal, and corresponding sides in one common ratio.
3. Drawing a similar figure
   40 min · 1 practice tasks · quiz
   Multiply every length by the scale factor and leave every angle alone.
4. Enlargement: a centre and a scale factor
   40 min · 1 practice tasks · quiz
   An enlargement happens about a fixed point, so where that point sits decides where the image lands.
5. Constructing the image
   40 min · 1 practice tasks · quiz
   Ray from the centre, measure, multiply, mark. Repeat for every vertex, then join.
6. Scale factors above, below and below zero
   40 min · 1 practice tasks · quiz
   The size of k sets the size of the image; the sign of k decides which side of the centre it lands on.
7. Finding the linear scale factor
   40 min · 1 practice tasks · quiz
   Divide an image length by the matching object length, then check with a second pair.
8. Similarity and enlargement in daily life
   40 min · 1 practice tasks · quiz
   Photographs, plans, models and the shadow of a tree all rest on the same idea.