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Similar Shapes Exploration
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Similar Shapes Exploration
Similar shapes have the same shape but may be different sizes. Their matching angles are equal, and their matching side lengths have the same scale factor. Show your working and include units where needed.
Spot the relationship
Use the properties of similar shapes to explain your choices.
1.Triangle A has side lengths 4 cm, 6 cm and 8 cm. Triangle B has side lengths 6 cm, 9 cm and 12 cm. Are the triangles similar? Explain how you know.
2.A designer enlarges a triangular badge. The original has angles 45°, 65° and 70°. What are the three angles in the enlarged badge?
3.A map-maker draws two similar rectangles. The smaller rectangle is 5 cm by 8 cm. The larger one has a shorter side of 15 cm. What is its longer side?
4.A photo is printed at twice its original size. The original photo is 7 cm wide and 10 cm tall. How wide and tall is the enlarged print?
5.A small pentagon has a side of 4 cm. Its matching side on a similar larger pentagon is 14 cm. What is the scale factor from the small pentagon to the large one?
Solve the scale-factor clues
For each problem, identify the scale factor before finding the missing length.
6.Two similar triangles have matching sides in the ratio 3:5 (small to large). A side of the smaller triangle is 12 cm. Find the matching side of the larger triangle.
7.A small triangle has sides 5 cm, 12 cm and 13 cm. A similar larger triangle has matching sides 15 cm, 36 cm and one unknown side. Find the unknown side.
8.A rectangle is 9 cm long and 6 cm wide. A similar rectangle has a width of 10 cm. Find its length.
9.A toy boat is a scale model of a real boat. The model is 18 cm long and the real boat is 6 m long. How many centimetres on the model represent 1 metre on the real boat?
10.Imogen says, “If two shapes have the same area, they must be similar.” Is Imogen correct? Give an example or explanation to support your answer.
Draw a rectangle that is similar to a 3 cm by 5 cm rectangle using a scale factor of 2. Label both side lengths.
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