Triangle Proportionality Theorem Worksheet
Explore and apply the Triangle Proportionality Theorem (also known as Thales's Theorem or the Basic Proportionality Theorem) to solve for unknown lengths in triangles and prove segment relationships.
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Triangle Proportionality Theorem
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Read each question carefully and solve for the unknown values using the Triangle Proportionality Theorem. Show all your work.
1. In ΔABC, DE || BC. If AD = 6, DB = 9, and AE = 8, find EC.
Show your work:
2. State the Triangle Proportionality Theorem: If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides .
3. In the diagram, PQ || RS. If TP = 10, PR = 4, and TQ = 12, find QS.
Show your work:
4. Which of the following conditions must be met to apply the Triangle Proportionality Theorem?
The triangle must be a right-angled triangle.
A line must be parallel to one side of the triangle.
The line must bisect one of the angles.
All sides of the triangle must be equal.
5. Given ΔXYZ with segment MN intersecting XY at M and XZ at N. If XM = 3, MY = 5, XN = 4, and NZ = 6, determine if MN || YZ. Justify your answer.
Justification: