Theorems Teacher Resources

Most adults remember learning about the Pythagorean theorem, but they don't all remember how to use it. The emphasis here is on developing an intuitive understanding of how and when to use the theorem. Young mathematicians explore...

Your class knows the Pythagorean Theorem, but can they prove it? A series of three videos shows two proofs of the Pythagorean Theorem and use it to classify triangles. 

Everyone's heard of Pythagoras, but who's Ptolemy? Learners test Ptolemy's Theorem using a specific cyclic quadrilateral and a ruler in the 22nd installment of a 23-part module. They then work through a proof of the theorem.

Amaze your classes with the ability to find side lengths of triangles immediately — they'll all want to know your trick! Learners use the Pythagorean Theorem and special right triangle relationships to find missing side lengths.

This unit on connecting algebra and geometry covers a number of topics including worksheets on the distance formula, finding the perimeter and area of polynomials, the slope formula, parallel and perpendicular lines, parallelograms,...

Use the given tasks and detailed teacher's commentary to introduce your 8th graders to the Pythagorean theorem and its converse. Embedded links to information about Egyptian geometry make your presentation interesting. Consider...

Students solve problems of dilation and velocity. In this geometry lesson, students apply the Pythagorean Theorem to solve problems and relate it to time and velocity.

In order to learn about the Pythagorean Theorem, young mathematicians investigate relations and patterns between different sides of a right triangle to look for possible relations among the squared sides. Once they have established the...

Students solve problems using the Pythagorean Theorem. For this geometry lesson, students identify the Pythagorean Triple and use it to solve real life problems.

Middle and high schoolers research the life of Pythagoras and the Pythagorean theorem. They write a short biography of Pythagoras and learn to apply the theorem in their study of right triangles.

There is more than one way to prove the Pythagorean Theorem. Euclid and Einstein found the same way to prove the Pythagorean Theorem. The video introduces several other ways to prove the theorem along with the history of its use.

There are many different ways to show a proof of the Pythagorean Theorem.  Here is a nice hands-on paper cutting activity that shows a graphic representation. You can even challenge your young Pythagoreans to come up with their own...

In this Pythagorean theorem worksheet, students use the Pythagorean theorem to find the missing unit of the triangle. Students solve 10 problems.

Inscribed angles are central to the lesson. Young mathematicians build upon concepts learned in the previous lesson and formalize the Inscribed Angle Theorem relating inscribed and central angles. The lesson then guides learners to prove...

Rolle with the mean values and derivatives. Scholars complete the statements of Rolle's Theorem and the Mean Value Theorem. Using the interactive to illustrate scenarios, pupils respond to questions concerning the theorems in terms of...

Learn to use the Pythagorean Theorem with non-right triangles. Pupils use the interactive to discover the relationship between the lengths of sides for acute and obtuse triangles. They compare the squares of the sides of the triangles to...

Don't keep this resource a secret. Individuals learn to use the Pythagorean Theorem to find Pythagorean triples. They also see how Pythagorean triples can be useful in the field of cryptography to encrypt secret messages.

Learners construct a variety of right triangles using a right-angled set square, cutting corners from pieces of paper or cardboard, and using dynamic geometry software. They measure the sides of these various right triangles and record...

Connect algebra and geometry on the coordinate plane. The eighth unit in a nine-part integrated course has pupils develop the distance formula from the Pythagorean Theorem. Scholars prove geometric theorems using coordinates...

The Pythagorean Theorem is a staple of middle school geometry. Scholars first investigate angle relationships, both in triangles and in parallel lines with a transversal, before proving and applying the Pythagorean Theorem.

The Hopewell people of the central Ohio Valley used right triangles in the construction of earthworks. Pupils use the Pythagorean Theorem to determine missing dimensions of right triangles used by the Hopewell people. The assessment task...

No geometry class is complete without a proof. A short video in the Socratica Geometry playlist covers an algebraic proof of the Pythagorean Theorem. Simplifying an equation with two equivalent expressions for the area of a square leads...

Use half the length to connect the midpoints. A section of a playlist on geometry introduces the concept of a midsegment of a triangle and how to find it. The video states the properties of the midsegment which make up the Midsegment...

Use the inside to find the outside. The resource presents two theorems dealing with exterior angles of a triangle. Using the two theorems, the segment from a larger geometry playlist works problems to solve for angle measures.