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.

### 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.

**Similar Triangles: Ratio of Areas**
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