Common Core: HSG-SRT.B.4
Theorems include: a line parallel to one side of a triangle
divides the other two proportionally, and conversely; the
Pythagorean Theorem proved using triangle similarity.
The following figures give the Triangle Proportionality Theorem and the Converse of the Triangle Proportionality Theorem. Scroll down the page for more examples and solutions.
Triangle Proportionality Theorem
The Triangle Proportionality Theorem
If a line parallel to one side of a triangle intersects the other
two sides, then it divides those sides proportionally. The segment
joining midpoints of two sides of a triangle is parallel to the
third side and half the length.
Using the Properties of the Triangle Proportionality Theorem to
Solve for Unknown Values
Proof: Converse of the Triangle Proportionality Theorem
Proving -- Converse of the Triangle Proportionality Theorem: If a
line divides two sides of a triangle proportionally, then it is
parallel to the third side.
Prove the Pythagorean Theorem using similar triangles
In this lesson, you will learn how to prove the Pythagorean Theorem
using similar triangles.
Pythagorean Theorem Proof Using Similarity
Proof of the Pythagorean Theorem using similarity.
Similar Triangles: Ratio of Areas
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