WOLFRAM|DEMONSTRATIONS PROJECT

The Ratio Theorem

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|AP| / |AB|
0.4
FractionBox[\(\(|\)\(AP\)\(|\)\), \(\(|\)\(PB\)\(|\)\)]​
≈
1.50
FractionBox[\(\(|\)\(AQ\)\(|\)\), \(\(|\)\(QC\)\(|\)\)]​
≈
1.50
In the triangle ABC let PQ be parallel to BC, with P on AB and Q on AC. Then |AP|/|PB| = |AQ|/|QC|.