# Prove Triangle Theorems

Videos, solutions, and lessons to help High School students learn how to prove theorems about triangles.

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.

Common Core: HSG-SRT.B.4

## 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.
Demonstration of the Triangle Proportionality Theorem
In the triangle ABC let PQ be parallel to BC, with P on AB and Q on AC. Then |AP|/|PB| = |AQ|/|QC|.

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.