1. 6.3a Using Similar Polygons Objective: Use proportions to identify similar polygons

2. Similar Same shape, not necessarily same size In order to be similar, angles must be congruent and corresponding side lengths proportional.

3. Insert Example 1 and GP 1

4. Scale Factor Ratio of lengths of two corresponding sides (stays consistent with all corresponding sides). *Pay attention to the order it asks for to give the correct scale factor.

5. Insert Example 2, 3, and GP 2, 3

6. Homework 6.3a 1 – 11, 40 – 48

7. 6.3b Objective: Use Similar Polygons Relationships with the scale factors

8. Review What is a scale factor? If ∆ABC ~ ∆DEF Which angles are congruent? What are the corresponding sides? What would a statement of proportionality look like? Extra Examples 1, 2, 3

9. GUIDED PRACTICE for Examples 2 and 3 In the diagram, ABCD ~ QRST. 2. What is the scale factor of QRST to ABCD ? 3. Find the value of x.

10. Perimeters of Similar Polygons If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.

11. EXAMPLE 4 Find perimeters of similar figures Swimming A town is building a new swimming pool. An Olympic pool is rectangular with length 50 meters and width 25 meters. The new pool will be similar in shape, but only 40 meters long. Find the scale factor of the new pool to an Olympic pool. a.

12. EXAMPLE 4 Find perimeters of similar figures Find the perimeter of an Olympic pool and the new pool. b.

13. EXAMPLE 4 Find perimeters of similar figures The perimeter of an Olympic pool is 2(50) + 2(25) = 150 meters. You can use Theorem 6.1 to find the perimeter x of the new pool. b.

14. GUIDED PRACTICE for Example 4 4.Find the scale factor of FGHJK to ABCDE. In the diagram, ABCDE ~ FGHJK. 5. Find the value of x. 6. Find The perimeter of ABCDE.

15. Similarity and Congruence If two figures are congruent, they are also similar, in which their scale factor would be _______.

16. Altitude and Median in a Triangle Median: page 319- Goes from a vertex to the midpoint of the opposite side Altitude: page 320- Goes from the vertex to the opposite side forming a perpendicular segment (think like the height of a triangle) In two similar triangles, these parts still use the scale factor

17. EXAMPLE 5 Use a scale factor In the diagram, ∆ TPR ~ ∆ XPZ. Find the length of the altitude PS.

18. GUIDED PRACTICE for Example 5 In the diagram, ∆JKL ~ ∆ EFG. Find the length of the median KM. 7.

19. Homework 6.3b 12, 14 – 28, 32, 33, 34, 36 Bonus: 29, 39