Revise Similar Triangles

Triangles that have exactly the same angles are similar.

If two angles match, the third angle will automatically match as the angle sum is always 180º.

Similar triangles have corresponding sides which are in the same ratio or proportion.

Here, the lengths of the sides in the right-hand triangle are 1.5 times the lengths of the matching sides in the left-hand triangle.

Example

Find the value of x from the information given in these triangles.

Answer

The triangles are similar because two angles match, and so will the third too.

Comparing corresponding sides, we get that the scale factor is 7 ÷ 5 = 1.4

x = 1.4 × 6 = 8.4 cm

Now it's over to you!