1. Similar Triangles by Tristen Billerbeck

2. Problem Solving in Geometry with Proportions
If x is the geometric mean
of a and b, then
Ex.1 Find the geometric mean between 12 and 3.
Ex.2 Find the geometric mean between 14 and 10.

3. Additional Properties of Proportions
False

5. True

6. Definition: Two polygons are similar if their angles are congruent and their sides are proportional. That common ratio is called the scale factor.
Scale factor =

7. Ex. Determine if the polygons are similar
Ex. Determine if the polygons are similar. If they are, write a similarity statement and find the scale factor.

8. Thm. If two polygons are similar, then their perimeters have the same ratio as the sides.

9. Ex. If the perimeter of STUVW is 100, find x and the perimeter of JKLMN.
Scale Factor

12. Proving Triangles are Similar
There are 3 postulates to prove that two triangles are similar:
 AA
 SSS
 SAS

13. Example 1

14. Example 2

15. Theorem 8.4: Triangle Proportionality Theorems
If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.
If JK ∥ HG, then
Theorem 8.5: Converse of the Triangle Proportionality Theorem
If a line divides two sides of a triangle proportionally, then it is parallel to the third side.
If , then JK ∥ HG.

16. Theorem 8.6
If three parallel lines intersect two transversals, then they divide the
transversals proportionally.
If r ∥ s and s ∥ t, and l and m intersect both r, s, and t, then r s t m Y U W l Z X V

17. Theorem 8.7:
If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides.
If bisects , then A D C B