1. Proportions
in Triangles

2. Side-Splitter Theorem
Theorem 7-4: Side-Splitter Theorem: If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally. OR

3. Side-Splitter Proof
Statements
Reasons 1. 2. 3. 4. 5. 6. 7.

4. Side-Splitter Theorem
Find the value of x.
Find the value of x.

5. Corollary to Side-Splitter Theorem
Corollary to Theorem 7-4: If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.

6. Application
Given that the edges of the panels of the sails are parallel, find the values of the variables.

7. You wanna try one? Too bad! ;)
Find the values of the variables in the following figure.

8. Triangle-Angle-Bisector Theorem
Triangle-Angle-Bisector Theorem: If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.

9. Triangle-Angle-Bisector Theorem
Find the value of x in the following figure.
Find the value of x in the following figure.

10. Kick it up a notch!!!
Find the value of x.

11. Kick it up a notch!!!
Find the value of x.