THEOREMS-SIMILAR POLYGONS

The focus so far has been on similar triangles, but there are also theorems that deal with similar____________ .

Polygons

Given: rectangle ABCD is similar to rectangle ZBXY. If ZY = 5, XC = 3, DC = 4, then XY =

2 1/2

Given: ABC is similar to XYC. If BY = 6, YC = 10, AX = 18, then XC =

30

One pair of corresponding sides of two similar polygons measures 12 and 15. The perimeter of the smaller polygon is 30. Find the perimeter of the larger.

37.5

A rectangular picture has dimensions 2½ by 1½. It is to be enlarged so that it is still similar to the original rectangle. If the longer dimension is now 10, how much longer than the original is the perimeter now?

4 times

The perimeters of two similar polygons are 20 and 28. One side of the smaller polygon is 4. Find the corresponding side of the larger polygon.

5 3/5

Given: rectangle ABCD is similar to rectangle ZBXY. If BA=8, BC=12 and the perimeter of rectangle BXYZ is 20, find BX.

6

Given: rectangle ABCD is similar to rectangle ZBXY. If BC = 10, BX = 6, XY = 4, then CD =

6 2/3

The smaller of two similar rectangles has dimensions 4 and 6. Find the dimensions of the larger rectangle if the ratio of the perimeters is 2 to 3.

6 by 9

Given: ABC is similar to XYC. If YC = 4, BC = 6, XY = 5, then AB =

7 1/2

Given: ABC is similar to XYC. If BY = 4, YC = 7, XC = 10. Which of the following proportions could be used to solve for AC?

7/11 = 10/AC

Two triangles have side lengths 3, 4, 5 and 6, _____, 10, respectively. The triangles are similar to each other.

8

The transitive property holds true for similar figures.

Always

The sides of a polygon are 3, 5, 4, and 6. The shortest side of a similar polygon is 9. Find the ratio of their perimeters.

1/3