Similar figures — Grade 7 Accelerated, what it means and where it is taught
Same shape, different size: equal angles, proportional sides.
Taught in Grade 7 Accelerated.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Proportional — Two quantities with a constant ratio: yx = k always.
What uses it later
This idea is needed for:
- Corresponding sides — Sides in matching positions in two similar figures.
Practise this idea
3 questions in the course bank use Similar figures, in Proportional Reasoning with Scale Drawings, Dilations & Similarity, Similarity & Proportionality.
Problem 1
Two similar figures have areas 25 cm2 and 64 cm2. The smaller has perimeter 20 cm. Find the larger perimeter.
Worked answer
32
k2 = 6425, so k = 85
Perimeter is a length, so it scales by k
20 × 85 = 32 cm
Problem 2
Which is always true for two similar figures?
- Corresponding angles are equal
- Corresponding sides are equal
- Perimeters are equal
- Areas are equal
Worked answer
Corresponding angles are equal
Angles never change under a dilation
Sides change by the factor k
So only the angle statement is always true
Problem 3
Two similar figures have sides in ratio 2:3. Find the ratio of their areas.
Worked answer
4:9
k = 32, so k2 = 94
Ratio 4:9