1. Add to your notes Corollaries
If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally.
If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

2. Agenda Homework Review Parts of Similar Triangles Fractals Homework
Flatland – 0 to 3 dimensions – Euclidean Geometry
Edwin A Abbott – Headmaster
1884
Flatterland – Euclidean & Non-Euclidean, Physics
Ian Stewart
2001

3. 7-4 Study Guide

4. 7-4 Practice

5. 7-4 Practice

6. 7-4 Practice

7. Parts of Similar Triangles
Proportional Perimeters Theorem
If two triangles are similar, then the perimeters are proportional to the measures of corresponding sides.

8. Example If LMN ~ QRS, QR = 40, RS = 41, SQ = 9 and LM = 9,
find the perimeter of LMN.

9. Example

10. Theorem
If two triangles are similar, then the measures of the corresponding altitudes are proportional to the measures of the corresponding sides.
BG AB =
EH DE
BG BC =
EH EF

11. Theorem
If two triangles are similar, then the measures of the corresponding angle bisectors of the triangles are proportional to the measures of the corresponding sides.
TA RT =
GB EG

12. Theorem
If two triangles are similar, then the measures of the corresponding medians are proportional to the measures of the corresponding sides.

13. Theorem Angle Bisector Theorem
An angle bisector in a triangle separates the opposite side into segments that have the same ratio as the other two sides. C
AD AC =
DB BC B A D

14. 7-6 Fractals and Self-Similarity
Iteration
A process of repeating the same procedure over and over.
Fractal
A geometric figure that is created using iteration.
Self-Similar
Smaller and smaller details of a shape have the same geometric characteristic as the original, larger form.
Strictly Self-Similar
All parts, no matter where they are located or no matter what size is selected, contain the same geometric figure as the whole.

15. Sierpinski’s Triangle
stage ?

16. Koch’s Curve
Stage 0
Stage 1
Stage 2
Stage 3

17. Koch’s Curve

18. Answers Ahead

19. 7-5 Study Guide

20. 7-5 Practice

21. 7-5 Practice

22. 7-5 Practice

23. 7-5 Practice

24. Homework
7-5 Study Guide & Practice
7-6 Study Guide & Practice