Side Splitter Theorem Worksheet

Side Splitter Theorem Worksheet

Read each question carefully and use the Side Splitter Theorem to solve for the unknown lengths. Show all your work.

1. In the triangle below, DE is parallel to BC. If AD = 6, DB = 9, and AE = 8, find the length of EC.

2. In \(\triangle PQR\), ST is parallel to QR. Given PS = 4 cm, SQ = 6 cm, and PT = 5 cm, find TR.

3. The Side Splitter Theorem states that if a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides  .

4. Another name for the Side Splitter Theorem is the  .

5. In \(\triangle XYZ\), AB is parallel to YZ. If XA = 3, AY = 5, and XB = 4, what is the length of BZ?

6. In trapezoid ABCD, with AB || CD, a line segment EF is drawn parallel to AB, intersecting AD at E and BC at F. If AE = 4, ED = 6, BF = 5, find FC.

7. A line parallel to side AB of triangle ABC intersects AC at D and BC at E. If CD = 10, DA = 5, and CE = 12, find EB.

8. The converse of the Side Splitter Theorem states that if a line divides two sides of a triangle proportionally, then it is parallel to the third side.