📚 Topic Summary
The Triangle Proportionality Theorem states that if a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally. Conversely, if a line divides two sides of a triangle proportionally, then it is parallel to the third side. This theorem is incredibly useful for solving problems involving similar triangles and unknown side lengths.
🧠 Part A: Vocabulary
Match the term with its definition:
- Parallel Lines
- Proportion
- Triangle
- Segment
- Ratio
- A part of a line that is bounded by two distinct end points.
- A comparison of two quantities.
- Lines in a plane which do not intersect or touch at any point.
- A closed shape with three sides and three angles.
- A statement that two ratios are equal.
✍️ Part B: Fill in the Blanks
Complete the paragraph with the correct terms:
The Triangle Proportionality Theorem involves a ______ cut by a line that is ______ to one of its sides. This line divides the other two sides into ______ segments. If the ratios of these segments are equal, we say they are in ______.
🤔 Part C: Critical Thinking
Explain in your own words how you can use the Triangle Proportionality Theorem to determine if two lines are parallel within a triangle. Provide an example.