Friday, December 22, 2006

Geometry 8.3+8.4 Similar polygons guided notes

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


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.