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Congruence & Similarity (Cambridge (CIE) IGCSE Maths)

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  • FrontCongruence

    Define the term congruent.

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  • Define the term congruent.

    Two shapes are congruent if they are identical in shape and size.

  • True or False?

    If one shape is an enlargement of the other, then they are congruent.

    False.

    If one shape is an enlargement of the other, then they are not identical in size and so are not congruent.

  • True or False?

    You need to show that two shapes are facing in the same direction to prove congruence.

    False.

    If the two shapes are identical in terms of shape and size then it does not matter which direction they are facing in.

  • Define the term similar shapes.

    Two shapes are similar if they have the same shape and their corresponding sides are in proportion.

    One shape is an enlargement of the other.

  • True or False?

    If two triangles of different sizes have the same angles they are not similar.

    False.

    If two triangles of different sizes have the same angles they are similar.

    One is an enlargement of the other.

  • True or False?

    Shapes that are not triangles can have the same angles and not be similar.

    True.

    Some shapes that are not triangles can have the same angles and not be similar.

    E.g. two rectangles of different sizes will have the same angles but their corresponding sides could have different scale factors.

  • True or False?

    To show that two non-triangular shapes are similar you need to show that their corresponding sides are in proportion.

    True.

    To show that two non-triangular shapes are similar you need to show that their corresponding sides are in proportion.

  • What is a scale factor, in the context of similarity?

    A scale factor is the ratio of corresponding lengths in similar shapes.

  • True or False?

    In the context of similarity, a scale factor cannot be negative.

    True.

    Although you can have a negative scale factor in general enlargement, in the context of similarity, a scale factor cannot be negative.

  • What does a scale factor that is greater than 0 but less than 1 imply?

    A scale factor that is greater than 0 but less than 1 implies that the similar shape is smaller than the original shape.

  • How can you find a length scale factor?

    A length scale factor can be found by dividing the length of a side on one shape by the length of a corresponding side on the similar shape.

  • What is the relationship between the length scale factor and the area scale factor?

    The area scale factor, k squared, is the square of the length scale factor k.

  • What is the relationship between the length scale factor and the volume scale factor?

    The volume scale factor, k cubed, is the cube of the length scale factor k.

  • True or False?

    The cube root of the volume scale factor can be used to find an unknown length.

    True.

    The cube root of the volume scale factor is the length scale factor. This can be used to find an unknown length.

    E.g. you can find length x by finding the volume scale factor, 448 over 56 equals 8, taking its cube root, cube root of 8 equals 2, and multiplying the result by the corresponding length on object A, x equals 7 cross times 2 equals 14 space cm.

    Two similar objects. Object A has a volume of 56 cm^3 and object B has a volume of 448 cm^3. The volume scale factor is therefore 8. A length of 7 cm is marked on object A and the corresponding length on object B is labelled x.

  • How do you find the area of a similar shape from a known area using the length scale factor, k?

    E.g. how can you find Area B in the diagram below?

    Two similar objects, A and B. Object A has a front surface area of 8 cm^2 and object B has a front surface area of x cm^2. One of the edges of object A has a length of 7 cm and the corresponding length on object B has a length of 14 cm.

    To find the area of a similar shape from a known area, find the length scale factor, k, and square it to find the area scale factor, k squared. Then multiply the result by the area of the shape you know.

    E.g. to find Area B, length space scale space factor equals 14 over 7 equals 2, so area space scale space factor equals 2 squared equals 4.
    Therefore, Area space straight B equals 8 cross times 4 equals 32 space cm squared.

    Two similar objects, A and B. Object A has a front surface area of 8 cm^2 and object B has a front surface area of x cm^2. One of the edges of object A has a length of 7 cm and the corresponding length on object B has a length of 14 cm.

  • True or False?

    Multiplying the cube root of the volume scale factor by an area can be used to find a corresponding area on a similar shape.

    False.

    Multiplying the cube root of the volume scale factor by an area can not be used to find a corresponding area on a similar shape.

    The cube root of the volume scale factor, is the length scale factor. This needs to be squared to find the area scale factor, which can then be used to find a corresponding area on a similar shape.

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