1. Parallel Lines and Proportional Parts
Triangle Proportionality Theorem
If a line parallel to one side of a triangle intersects the other two sides in different points, then it divides those sides proportionally.
Converse of the Triangle Proportionality Theorem
If a line intersects two sides of a triangle in different points and divides those sides proportionally, then it is parallel to the third side.

2. In and Find BY. B
Answer:
Example 4-1c

3. In and AZ = 32. Determine whether Explain.
Answer: No; the segments are not in proportion since
Example 4-2c

4. Parallel Lines and Proportional Parts
Midsegment of a triangle – A line segment that connects the midpoints of two of its sides.
Triangle Midsegment Theorem
The segment that joins the midpoints of two sides of a triangle is parallel to the third side and its length is half the length of the third side.

5. Triangle UXY has vertices U(–3, 1), X(3, 3), and Y(5, –7)
Triangle UXY has vertices U(–3, 1), X(3, 3), and Y(5, –7) is a midsegment of
Example 4-3h

6. a. Find the coordinates of W and Z. b. Verify that
c. Verify that
Answer: W(0, 2), Z(1, –3)
Answer: Since the slope of and the slope of
Answer: Therefore,
Example 4-3i

7. Parallel Lines and Proportional Parts
Corollaries
6.1 – If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally.
6.2 – If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

8. In the figure, Davis, Broad, and Main Streets are all parallel
In the figure, Davis, Broad, and Main Streets are all parallel. The figure shows the distances in city blocks that the streets are apart. Find x.
Answer: 5
Example 4-4c

9. Find a and b.
Answer: a = 11; b = 1.5
Example 4-5d