1. Parallel Lines and Proportional Parts Write the three ratios of the sides given the two similar triangles.

2. It is also true that the two parts of each side are proportional. Triangle Proportionality: If a line is parallel to one side of a triangle and intersects the other two sides, then it separates these sides into segments that are proportional.

3. This means, we could write another set of equal ratios…

4. Solve for x and y.

5. Given the picture, if M and N are midpoints, find the value of x.

6. This shows us the next property about similar triangles. Thm 7.6: If you connect the midpoints of two sides of a triangle, then the length of that segment is ½ the length of the third side of the triangle.

7. Ex. In ∆ABC, M is the midpoint of AB, N is the midpoint of BC and P is the midpoint of AC. Find the perimeter of ∆MNP if AB = 16, BC = 18 and AC = 22.

8. Corollary: If three or more parallel lines are cut by two transversals, then they are cut proportionally.