Question

The following triangles are similar. Find side AB.

2



4



10



12

Answer 1

X+2=6
X=6-2
X=4
Because side length are similar so the length must be equal

Answer 2

4

Explanation:

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion. In other words, similar triangles are the same shape, but not necessarily the same size.

If a triangle ABC is similar to another triangle DEF, then the following equation is true:

`(AB)/(DE) =(BC)/(EF) = (CA)/(FD)`

Therefore:

`(AB)/(DE) =(BC)/(EF)\\\\(x+2)/(6) =(2)/(3)`

Solving for x:

`x=2`

The segment AB is:

`AB=x+2\\\\Where\\\\x=2\\\\Hence\\\\AB=2+2=4`