Triangle Proportionality Theorem Worksheet

Triangle Proportionality Theorem

Read each question carefully and apply the Triangle Proportionality Theorem to find the missing lengths. Show all your work.

1. State the Triangle Proportionality 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 converse of the Triangle Proportionality Theorem states that if a line divides two sides of a triangle proportionally, then it is   to the third side.

4. In \u25b3ABC, if DE || BC, AD = 6, DB = 3, and AE = 8, what is EC?

5. In \u25b3PQR, ST || QR. If PS = 10, SQ = 4, and PT = 15, find TR.

6. A triangle has vertices at A(1, 2), B(7, 2), and C(4, 8). A line segment DE is drawn parallel to AB, with D on AC and E on BC. If AD is 1/3 of AC, find the coordinates of D and E.

7. If a line divides two sides of a triangle proportionally, it must be parallel to the third side.