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
3x = 50
x = 50/3
If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.