Triangle Proportionality Theorem Worksheet
Explore the Triangle Proportionality Theorem with this worksheet for 8th graders, featuring problems on segment lengths and parallel lines within triangles.
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Triangle Proportionality Theorem
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. State the Triangle Proportionality Theorem (also known as Thales's Theorem or the Basic Proportionality Theorem) in your own words.
2. In triangle ABC, if a line parallel to side BC intersects sides AB and AC at D and E respectively, then it divides the two sides .
3. In the triangle above, if AD = 6, DB = 9, and AE = 4, find the length of EC.
EC =
4. In the same triangle, if AD = 5, AB = 15, and AE = 3, find the length of AC.
AC =
5. Which of the following conditions must be true for the Triangle Proportionality Theorem to apply?
The triangle must be a right triangle.
The line segment must be perpendicular to one side.
The line segment must be parallel to one side.
The triangle must be equilateral.
6. The converse of the Triangle Proportionality Theorem states that if a line divides two sides of a triangle proportionally, then it is parallel to the third side.
True
False
7. Consider a triangle ABC. A line DE is drawn parallel to BC, intersecting AB at D and AC at E. If AD = x, DB = x - 2, AE = x + 2, and EC = x - 1, find the value of x.