What is the Side Splitter Theorem? A Complete Introduction and Exploration
The side splitter theorem says a line parallel to one side of a triangle divides the other two sides proportionally. It follows from similar triangles, and it works in reverse to prove lines parallel.
Worked examples: the side splitter theorem
Practice questions on the side splitter theorem
- In triangle (ABC), line segment (DE) is parallel to (BC). If (BD = 6 text{ cm}), (DA = 18 text{ cm}), and (AE = 9 text{ cm}), find (CE).
- Given triangle (PQR), line segment (ST) is parallel to (QR), ( ST ) divides (PR) into (PT) and (TR) in the ratio 2:3. If (QR = 15 text{ cm}), find (ST).
- (CE = 3 text{ cm})
- (ST = 6 text{ cm})
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