Prove Triangle Theorems

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.

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Using the Properties of the Triangle Proportionality Theorem to Solve for Unknown Values

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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.

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Pythagorean Theorem

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.

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Similar Triangles: Ratio of Areas

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