📚 Topic Summary
The Converse of the Triangle Proportionality Theorem states that if a line divides two sides of a triangle proportionally, then that line is parallel to the third side. In simpler terms, if you have a triangle and a line cutting through two of its sides, and the ratios of the segments created on each of those sides are equal, then that line is parallel to the triangle's base. This is a powerful tool for proving lines are parallel!
For example, if in triangle $ABC$, a line intersects $AB$ at $D$ and $AC$ at $E$, and $\frac{AD}{DB} = \frac{AE}{EC}$, then line $DE$ is parallel to line $BC$.
🧠 Part A: Vocabulary
Match the terms on the left with their definitions on the right:
| Term |
Definition |
| 1. Triangle |
a. A line that cuts across two or more lines |
| 2. Parallel Lines |
b. A closed figure with three sides and three angles |
| 3. Proportional |
c. Having the same or a constant ratio |
| 4. Converse |
d. Two lines in the same plane that never intersect |
| 5. Transversal |
e. A statement formed by reversing the hypothesis and conclusion of another statement |
✏️ Part B: Fill in the Blanks
Complete the paragraph using the words: parallel, proportional, triangle, sides, Converse.
The ______ of the Triangle Proportionality Theorem states that if a line divides two ______ of a ______ proportionally, then the line is ______ to the third side. In other words, if the ratios of the segments are equal, the lines are ______.
🤔 Part C: Critical Thinking
Explain in your own words why the Converse of the Triangle Proportionality Theorem is useful in geometry.
