Similar shapes & congruence
AQA GCSE Maths revision on Similar shapes & congruence. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
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Question 1
Two triangles have identical interior angles but different side lengths. Which term best describes their relationship?
- A) Congruent
- B) Similar
- C) Equilateral
- D) Isosceles
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Answer: Similar
Similarity refers to shapes that have the same shape and proportions but not necessarily the same size. Congruence requires the shapes to be identical in both size and shape, whereas similarity only requires the angles to match.
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Question 2
A student claims that if two rectangles have the same perimeter, they must be congruent. Why is this incorrect?
- A) Perimeter only considers the boundary, not the interior angles
- B) Congruence requires identical side lengths, not just equal perimeters
- C) The area must also be identical to prove congruence
- D) Perimeter is a property of similarity, not congruence
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Answer: Congruence requires identical side lengths, not just equal perimeters
Congruence means the shapes are identical in every way, meaning all corresponding sides and angles must be equal. A 2x4 rectangle and a 1x5 rectangle both have a perimeter of 12, but they are clearly not congruent.
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Question 3
If the scale factor between two similar shapes is 1, what can you conclude about the two shapes?
- A) They are similar but not congruent
- B) They are congruent
- C) They are reduced in size
- D) They are enlarged in size
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Answer: They are congruent
When the scale factor of similarity is 1, the dimensions of the image are identical to the object. Therefore, the shapes are not only similar but also congruent.
Want to test yourself on the remaining cards for this topic?
13 more questions on Similar shapes & congruence — plus mistakes tracking and spaced repetition across the whole Maths spec.