Side Splitter Theorem Worksheet

Side Splitter Theorem

Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. State the Side Splitter Theorem in your own words.

2. If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides  .

3. The Side Splitter Theorem is also known as the   Theorem.

4. In triangle ABC, a line DE is parallel to BC, intersecting AB at D and AC at E. If AD = 4, DB = 6, and AE = 5, what is the length of EC?

5. Consider a triangle PQR. A line ST is parallel to QR, with S on PQ and T on PR. If PS = 3x, SQ = x + 2, PT = 12, and TR = 8, find the value of x.

6. A transversal intersects three parallel lines, creating segments of length 5 cm and x cm on one transversal, and 8 cm and 12 cm on the other transversal. Find the value of x.

7. 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.