Triangle Proportionality Calculator
If DE ∥ BC, then AD/DB = AE/EC
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Triangle Proportionality Theorem
AD/DB = AE/EC
(when DE is parallel to BC)
Diagram
Understanding the Triangle Proportionality Theorem
The Triangle Proportionality Theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally.
The Theorem
If DE ∥ BC in triangle ABC, then:
AD/DB = AE/EC
Equivalently: AD/AB = AE/AC and DB/AB = EC/AC
The Converse
If a line divides two sides of a triangle proportionally, then it is parallel to the third side.
If AD/DB = AE/EC, then DE ∥ BC
Special Case: Midsegment
When D and E are midpoints, AD/DB = AE/EC = 1, and DE is called a midsegment. The midsegment is parallel to the third side and half its length.
Frequently Asked Questions
What is the Triangle Proportionality Theorem?
If a line parallel to one side of a triangle intersects the other two sides, it divides them proportionally: AD/DB = AE/EC.
How do I check if a line is parallel?
Use the converse: calculate AD/DB and AE/EC. If they're equal, the line is parallel to the third side.
What is a midsegment?
A midsegment connects the midpoints of two sides. It's parallel to the third side and half as long. It's a special case of the proportionality theorem.
Can I use this with similar triangles?
Yes! When DE ∥ BC, triangle ADE is similar to triangle ABC. The proportionality theorem follows from this similarity.
What are other equivalent proportions?
AD/AB = AE/AC, DB/AB = EC/AC, and AD/AE = DB/EC are all equivalent forms of the same relationship.