(7-2) Exploring Similar Polygons


Obj: To identify similar figures and to solve problems

involving similar figures.


Similar polygons (~) Two polygons are similar if their corresponding angles are congruent and the measures of their corresponding sides are proportional.









Scale Factor: The ratio of the lengths of any two corresponding sides.










Trapezoid ABCD ~ Trapezoid ZYXW


Find the scale factor:


Find the value of x:



Ex. 3) If quadrilateral ABCD is similar to quadrilateral EFGH, Find each of the following.



A) scale factor of ABCD to EFGH.








E) Perimeter of ABCD


F) Perimeter of EFGH


G) Ratio of the perimeter of

ABCD to the perimeter of




Ex. 4) Each pair of polygons is similar. Find the value of x and y.


A) B)










Ex. 5) Quadrilateral RSTV is similar to quadrilateral LMNO. The sides of RSTV are 6, 10, 12, and 14 inches long. The shortest side of LMNO is 9 inches long.


a) What is the scale factor of RSTV to LMNO?


b) Find the two longest sides of LMNO.


c) Find the perimeter of LMNO.


d) What is the ratio of the perimeters of RSTV and LMNO?




Ex. 6) Triangle ABC has vertices A(0, 0), B(3, 0) and C(0,4). If the coordinates are multiplied by 3, will

the new triangle be similar to triangle ABC? Why or why not?