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
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.