Curated OER
Who Dun It?
In this proofs by contradiction worksheet, students solve 1 word problem about a crime. Students use proof by contradiction to determine the criminal in the word problem.
Curated OER
Indirect Proof and Inequalities in one Triangle
In this geometry worksheet, 10th graders complete an indirect proof and order the sides or angles of a triangle. Also, students determine if a triangle can have sides with the given lengths. The two page worksheet contains twelve...
EngageNY
The Converse of the Pythagorean Theorem
Is it a right triangle or not? Introduce scholars to the converse of the Pythagorean Theorem with a lesson that also provides a proof by contradiction of the converse. Pupils use the converse to determine whether triangles with given...
Curated OER
The Truth About Triangles And Proofs
High schoolers engage in a lesson that is about the classification of triangles and the mathematical proofs involved in working with them. They work on a variety of problems that are created by the teacher with the focus upon the...
EngageNY
There is Only One Line Passing Through a Given Point with a Given Slope
Prove that an equation in slope-intercept form names only one line. At the beginning, the teacher leads the class through a proof that there is only one line passing through a given point with a given slope using contradiction. The 19th...
Curated OER
Three for the Money: The Degree/Diameter Problem
Pupils explore the concept of vertex-edge graphs. In this vertex-edge graphs lesson, students try to construct a graph with a given diameter, number of vertices, size, and planarity. Pupils construct various vertex-edge...
EngageNY
Converse of the Pythagorean Theorem
Discover a new application of the Pythagorean Theorem. Learners prove and apply the converse of the Pythagorean Theorem in the 17th instructional activity in a 25-part series. The examples ask learners to verify right triangles...
Beauty and Joy of Computing
Unsolvable and Undecidable Problems
Try as you might, some functions just cannot be computed. The lab introduces the class to the possibility of unsolvable problems. The fourth lesson in a series of seven begins with a logic problem, then progresses to looking at functions...
Curated OER
Investigating AAS
Students investigate the theorems of ASA, AAS, AAA and ASA. In this geometry lesson, students discuss the theorems of triangles and how it is used to solve for missing sides or angles. They review how two angles are formed by two rays...
Curated OER
Complex Analysis: Theorems Following Cauchy's Integral Formulas
For this integral formula, students explore how theorems are derived. They write proofs supporting Cauchy's Inequality, Liouville's Theorem, the Fundamental Theorem of Algebra, Gauss' Mean Value Theorem and Cauchy's Residue Theorem. ...
Illustrative Mathematics
Applying the Pythagorean Theorem in a Mathematical Context
Participants who use this resource will apply the Pythagorean Theorem to show whether or not the shaded triangle inscribed in a rectangle is a right triangle. Once all of the sides on the shaded triangle are found, it is important that...
Curated OER
Babylonian Mathematics 2
Students research Babylonian mathematics. They calculate simple surd numbers. Students find the fractional form of rational numbers expressed as decimals. They work with numbers in base 60.
Curated OER
ESL: "As Long As," "Providing That," and "Unless"
In this ESL grammar worksheet, students fill in blanks in sentences to correctly complete, using either "as long," "providing" or "unless." Students then write original sentences using these phrases.
Education Development Center
Making Mathematics: Proof
This is a site which links to specific techniques of proving including conditional statements, proof by contradiction, mathematical induction, parity arguments, and the pigeonhole principle. The site contains a link to various example...
Oswego City School District
Regents Exam Prep Center: Indirect Euclidean Proofs
This Oswego City School District Regents Exam Prep site shows you how to proof something by showing that it is false. This look at indirect proofs includes a practice and a teacher resource page, which features a warm-up activity.
Mathigon
Mathigon: Axioms and Proof
Explore this course in logic, sets, and proof including topics of axioms, set theory, and proof by contradiction and induction.
CK-12 Foundation
Ck 12: Geometry: Indirect Proof in Algebra and Geometry
[Free Registration/Login may be required to access all resource tools.] This concept teaches students how to write an indirect proof and provides examples of indirect proofs in Algebra and Geometry.
CK-12 Foundation
Ck 12: Geometry: Indirect Proof in Algebra and Geometry
[Free Registration/Login may be required to access all resource tools.] Write algebraic and geometric indirect proofs.
Kent State University
Kent State University: Indirect Proofs, Michael Byron
Use this site to explore an excellent discussion of indirect proofs. The site explains in detail why such a method works as a proof and gives steps to obtain such a proof.
Other
Platonic Realms: Conic Sections
A proof to show that the square root of two is an irrational number, followed by a shorter and even more beautiful proof.
Other
California State University, Fresno: Counter Examples
Come see how a counter example is helpful in some proofs. The site explains what a counter example says, and then offers a proof using a counter example.