8.3 Similar Polygons

Objectives:Identify similar polygonsUse similar polygons to solve real-life problems

Identifying similar polygons

Remember our AAA triangles?They were not congruent if none of the

sides were congruent.But they are similar.

Identifying similar polygons

When there is a correspondence between 2 polygons such that their corresponding angles are congruent and the lengths of corresponding sides are proportional, the 2 polygons are called similar polygons.

The symbol ~ is used to show similarity: ABCD ~ QRST

Look at Example 1 on p. 473

Pentagons JKLMN and STUVW are similar.

List all the pairs of congruent angles.Write the ratios of the corresponding sides

in a statement of proportionality.

Look at Example 2 on p. 473

Are these 2 quadrilaterals similar? What is the ratio of the larger to the

smaller?

Look at Example 3 on p. 474

If you enlarge a 3.5 by 5 photograph to a 16 by x poster, what is x?

X = 16 * 5 3.5X = 22.9

Scale Factor

If 2 polygons are similar, then the ratio of the lengths of 2 corresponding sides is called the scale factor.

For example 2, this was 3:2What is the scale factor of the patio to the

pool on p. 474?

Theorem

If 2 polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.

Try some . . .

P. 475 #2-7P. 477 #31-38P. 477 # 43 & 44P. 480 Example 1

Angle Angle Similarity Postulate

If 2 angles of 1 triangle are congruent to 2 angles of another triangle, then the 2 triangles are similar.

For example, look at the picture of the tourmaline crystal on p. 481.

What do you know? How can you use this to prove they are

similar?

Why does a line have only one slope, no matter which 2 points you look at?

Look at the picture on the bottom of p. 481. Triangle AFD is similar to triangle BEC.The changes of y (EC and FD) are proportional.The changes of x (AF and BE) are proportional.Change of y over change of x will be the same

(the slope)

Look at p. 482 Example 4

Homework: Worksheets