How do you find the value of x in a pair of similar polygons?
If x is a side, set up a proportion. You are usually given four pieces of information all together (maybe 3 numbers and x, maybe 2 numbers and two expressions of x). Corresponding sides go in the same fractions. For example, say triangles ABC and DEF are similar. Then you know sides AB/DE = BC/EF.
If x is an angle, corresponding angles are equal. So, for triangles ABC and DEF, angleABC = angleDEF.
You set up a proportion. The similar sides set equal to each other.
To prove similarity, corresponding angles must be the same, and also the ratio of the corresponding sides must be proportional, meaning a/b and c/d must get the same value.
So, if x is an angle, you will get information like 2 known angle values and one unknown angle value, or all three known angle values. angle a= angle b
If x is an length, you will get three sides of any polygon being proportionate to the corresponding sides of another similar polygon or only two pairs of corresponding sides a/b=c/d