Similar triangles/Finding unknown lengths

General Information
'Recognise when shapes are similar and use proportional reasoning to ﬁnd an unknown length.' Is a bullet point under Geometry and Measurement in Mathematics and Statistics, Level 6. Note that although it refers to similar 'shapes', this will mostly be focused around similar triangles. Assessment of this requirement is usually either in simple questions or as part of a more complex one.

What you need to know
Two triangles are similar if they are of the same shape (they do not have to be the same size!), i.e. one is the enlargement of another. This means that 1: all three angles of one triangle will be of the same size as the corresponding angle on the other triangle. and 2: the length of all three sides of one triangle will be in proportion to the corresponding sides on the other triangle.

You can tell that two triangles are similar if:

Two pairs of angles are of the same size.

Two pairs of sides' lengths are in proportion to each other, and the angles in between them are identical in size.

All three pairs of side lengths are in proportion to each other.

Congruent triangles have, by definition, the same shape and size as each other and therefore are considered similar.

To calculate the length of an unknown side, first determine which side corresponds to which, i.e, which side is in proportion to each other. Using the example of (1) above, side AD would be proportionl to side AB, and side AE would be proportional to side AC. AD/AB would be equal to AE/AC. Note here that both of the shorter sides are numerators while the longer sides are denominators. ''Do not confuse the corresponding sides. ''Suppose sides AD, AB and AE were known and you were required to find AC. AD/AB would give you a ratio, which you can then use in: (Aforementioned ratio)=AE (Known)/AC. The resulting equation would be an easily solved linear equation.

A useful thing to do is to arrange points of triangles so that they correspond with one another to avoid confusion. Using the example of (6) above, we would call the triangles △ADE and △ACB, instead of another, more confusing combination like △AED and △BCA.

Links
Due to the difficulty of creating a picture in the Wikia format, no practice questions have been provided. The following are some links you may find helpful:

https://www.khanacademy.org/math/geometry/hs-geo-similarity/hs-geo-solving-similar-triangles/e/solving_similar_triangles_1 (practice questions with no registration required)

https://www.sophia.org/tutorials/solving-for-unknown-sides-of-similar-triangles--2 (video tutorial and quiz)

https://www.mathopenref.com/similartriangles.html (fun dragging activity)