Identify Similar Shapes and Find Missing Lengths

Similar shapes have matching corresponding angles and corresponding sides which are in the same ratio.

In these two triangles, the angles are equal, and you will notice that the second triangle has sides which are twice the length of the sides of the first triangle. There is a scale factor of 2.

The smaller triangle has a length of 3 cm. If we use the scale factor of 2, we get 3 x 2 = 6  for the length of the bigger triangle.

The smaller triangle has a height of 7 cm. If we apply the scale factor of 2, we get 7 x 2 = 14 for the height of the bigger triangle.

If we have two similar shapes and one of the lengths is not given, we can use the scale factor to find the missing length.

For example, if we have two similar triangles and we know the heights of them are 4 cm and 12 cm respectively, we can see that the scale factor must be 3 because

4 x 3 = 12

We can apply this scale factor to find any missing lengths. If the smaller triangle has a length of 5 cm, then we can do 5 x 3 = 15, so we know that the bigger triangle has a length of 15 cm.

Let's have a go at some questions now.