A. Similar polygons - If all **corresponding angles** are **congruent** and all **corresponding sides** are proportional, then the polygons are similar.

Example: **If quadrilateral ABCD and quadrilateral DFGH have the following relationship**:

angle A = angle D, angle B = angle F, angle C = angle G, angle D = angle H, and

(AB)/DF = BC/FG = CD/GH = AD/DH,

then we know **quadrilateral ABCD ~ quadrilateral EFGH**.

B. Statement of Proportionality: Set up **ratios **using corresponding sides. These ratios are all **proportional.**

Example: Pentagon ABCDE ~ Pentagon FGHIJ

Because the pentagons are similar, we know angle A = angle F, angle B = angle G, angle C = angle H, angle D = angle I, angle E = angle J and

AB/FG = BC/GH = CD/HI = DE/IJ = AE/FJ

C. Using scale factors: Set up a **ratio** using a pair of corresponding sides. Reduce, if possible.

Example: If you want to enlarge a picture that is 3” in width by 5” in length and have the corresponding width of the enlarged picture be 10”, what is the new length?

3/5 = 10/x

3*x* = 50

*x* = 50/3

**If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar**.