Sect. 8.3 Similar Polygons Goal 1 Identifying Similar Polygons Goal 2 Using Similar Polygons in Real Life

Identifying Similar Polygons Similar polygons are polygons for which all corresponding angles are congruent and all corresponding sides are proportional.  Example:

Similar Polygons Polygons are said to be similar if : Identifying Similar Polygons Similar Polygons Polygons are said to be similar if : a) there exists a one to one correspondence between their sides and angles. b) the corresponding angles are congruent and c) their corresponding sides are proportional in lengths.

Identifying Similar Polygons Definition of Similar Polygons - Two polygons are SIMILAR if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional.

Identifying Similar Polygons In the diagram, pentagon GHIJK is similar to (~) pentagon ABCDE, if all corresponding angles are congruent GHIJK ~ ABCDE

Find the value of x, y, and the measure of P if TSV ~ QPR. Identifying Similar Polygons Example 1 Find the value of x, y, and the measure of P if TSV ~ QPR. x = 6 y = 10.5 P = 86°

Example 2 A  P, B  Q, C  R, D  P Using Similar Polygons in Real Life Example 2 Trapezoid ABCD is similar to trapezoid PQRS. List all the pairs of congruent angles, and write the ratios of the corresponding sides in a statement of proportionality. A  P, B  Q, C  R, D  P

Decide if the triangles are similar. Using Similar Polygons in Real Life Example 3 Decide if the triangles are similar. If they are, give the similarity statement. The triangles are not similar.

Using Similar Polygons in Real Life Example 4 You have a picture that is 4 inches wide by 6 inches long. You want to reduce it in size to fit a frame that is 1.5 inches wide. How long will the reduced photo be?

/ A  / E; / B  / F; / C  / G; / D  / H Using Similar Polygons in Real Life Scale factor: The ratio of the lengths of two corresponding sides of similar polygons / A  / E; / B  / F; / C  / G; / D  / H AB/EF = BC/FG= CD/GH = AD/EH The scale factor of polygon ABCD to polygon EFGH is 10/20 or 1/2

Using Similar Polygons in Real Life Scale Factor The common ratio for pairs of corresponding sides of similar figures Example:                            

In figure, there are two similar triangles . D LMN and D PQR. Using Similar Polygons in Real Life In figure, there are two similar triangles . D LMN and D PQR. This ratio is called the scale factor. Perimeter of D LMN = 8 + 7 + 10 = 25 Perimeter of D PQR = 6 + 5.25 + 7.5 = 18.75

Using Similar Polygons in Real Life Theorem 8.1 If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding sides. If ABCD ~ SPQR, then

Using Similar Polygons in Real Life Example 5 Parallelogram GIHF is similar to parallelogram LKJF. Find the value of y. Y = 19.2