1. Lesson 8.8 Similar Polygons
Essential Question: How do you find missing measures in similar polygons?

2. Before we start…
Jay is 72 inches tall and casts a 48 inch shadow. At the same time, a tree casts a 72 inch shadow. The triangles formed are similar. A photograph is taken of Jay standing next to the tree. In the photograph, the image of the tree’s shadow is 2 inches.
What is the height of the tree?
2. In the photograph, what is the height of the tree’s image?
3. In the photograph, what is the height of Jay’s image?

3. What are similar figures?
Figures that have the same shape, but not the same size ~
You identify corresponding parts in similar figures

4. What are corresponding parts?
The sides or angles that have the same relative position in similar figures

7. How do you identify similar figures?
Check to see if they have the same shape.
Check that corresponding angles are congruent.
Check that corresponding sides are proportional.

8. Given ∆𝐿𝑀𝑁~∆𝑃𝑄𝑅, name the corresponding angles and the corresponding sides.

9. Given 𝐴𝐵𝐶𝐷~𝑊𝑋𝑌𝑍, name the corresponding angles and the corresponding sides.

10. Given ∆𝑆𝑇𝑈~∆𝑉𝑊𝑋, name the corresponding angles and the corresponding sides.

11. Given 𝐴𝐵𝐶𝐷~𝐽𝐾𝐿𝑀, find the ratio of the lengths of corresponding sides of ABCD to JKLM.

12. Given 𝐹𝐺𝐻𝐽~𝐾𝐿𝑀𝑁, find the ratio of the lengths of corresponding sides of FGHJ to KLMN.

13. Given 𝐴𝐵𝐶𝐷~𝑄𝑅𝑆𝑇, find the ratio of the lengths of corresponding sides of ABCD to QRST.

14. A soccer field is a rectangle that is 70 yards long and 40 yards wide
A soccer field is a rectangle that is 70 yards long and 40 yards wide. The penalty area of the soccer field is a rectangle that is 35 yards long and 14 yards wide. Is the penalty area similar to the field?

15. The top of Selena’s rectangular dining room table measures 60 inches by 108 inches. She has a matching rectangular coffee table whose top measures 18 inches by 48 inches. Are the two tables similar?

16. How do you find missing measures in similar polygons?
Corresponding angles are congruent.
Corresponding sides are proportional so set up a proportion to find a missing side length.

17. In the diagram, ∆𝑃𝑄𝑅~∆𝑆𝑇𝑈. What is the value of y?

18. In the diagram, Trapezoid 𝐸𝐹𝐺𝐻~ Trapezoid 𝑀𝑁𝑄𝑃
In the diagram, Trapezoid 𝐸𝐹𝐺𝐻~ Trapezoid 𝑀𝑁𝑄𝑃. What is the value of x and y?

19. In the diagram, Quadrilateral 𝑃𝑄𝑅𝑆~ Quadrilateral 𝑊𝑋𝑌𝑍
In the diagram, Quadrilateral 𝑃𝑄𝑅𝑆~ Quadrilateral 𝑊𝑋𝑌𝑍. What is the value of x?

20. In the diagram, ∆𝐴𝐵𝐶~∆𝐸𝐹𝐺. What is the value of x?

21. Alma is 5 feet tall and casts a 7 foot shadow
Alma is 5 feet tall and casts a 7 foot shadow. At the same time, a tree casts a 14 foot shadow. The triangles formed are similar. Find the height of the tree.

22. A building is 25 feet tall and casts a 10 foot shadow
A building is 25 feet tall and casts a 10 foot shadow. At the same time, a fence casts a 6 foot shadow. The triangles formed are similar. Find the height of the fence.

23. You are making a gingerbread house that is similar in shape to a real house. The real house is 25 feet tall and 40 feet wide. The gingerbread house is 2.5 feet tall. How wide should you make the gingerbread house?

24. How do you find missing measures in similar polygons?

25. Ticket Out the Door
Quadrilateral WXYZ is similar to Quadrilateral LMNP. Find the values of x and y.