National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Building Two Column Proofs
Use this site to find details of how to construct a two column proof. Dr. Math responds to a question posed by a student and details the reasons for the order of steps and shows two different ways to do the same proof.
Science Buddies
Science Buddies: Inscribing a Circle in a Triangle Using the Geometry Applet
Here is a project that combines Computer Science and Mathematics. Prove a method for inscribing a circle within a triangle (as shown). You'll also learn how to create an interactive diagram to illustrate your proof, using an applet that...
Other
Math Court: A Game of Proving Things
This site contains a game to help students better learn how to write proofs. The game has several different levels. The game can be played online or cards and board may be printed and used in the classroom.
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.
CK-12 Foundation
Ck 12: Geometry: Proofs Study Guide
[Free Registration/Login may be required to access all resource tools.] This study guide reviews proofs: algebraic proof, properties of congruence, and geometric proofs (two-column).
CK-12 Foundation
Ck 12: Interactive Geometry: 4.1 Theorems and Proofs
Understand theorems and proofs as they relate to geometry.
Math Planet
Math Planet: Geometry: Proofs Using Algebra
Examples and a video lesson help to explain proofs and logic. [1:57]
Oswego City School District
Regents Exam Prep Center: Styles of Proof
Find out the general form for two column proofs, flow proofs, and paragraph proofs here. The site is very brief and discusses each type of proof using the same example.
CK-12 Foundation
Ck 12: Interactive Geometry: 11.1 Descriptions of Events
In a coordinate proof, geometric statements using algebra and the coordinate plane.
CK-12 Foundation
Ck 12: Geometry: Types of Reasoning Study Guide
[Free Registration/Login may be required to access all resource tools.] Reasoning is a fundamental part of geometric proofs. There are several types of reasoning, many of which we innately and naturally picked up. However, the different...
National Council of Teachers of Mathematics
Nctm: Illuminations: Proof Without Words: Completing the Square
Use this interactive geometric proof to complete the square using geometry.
National Council of Teachers of Mathematics
Nctm: Illuminations: Proof Without Words: Pythagorean Theorem
This applet proves the Pythagorean Theorem "without words" using geometry.
Mathigon
Mathigon: Euclidean Geometry: Euclid's Axioms
This lesson focuses on Euclid's Axioms, simple, intuitive statements, that everyone agrees are true. An axiom(or postulate) is a mathematical statement that is regarded as "self-evident" and accepted without proof. A key part of...
Other
Propagation of Light Using Geometry
A discussion of Christian Huygens' contribution to wave optics, and particularly to our understanding of the reflection and refraction of light. Excellent diagrams and a geometric proof on why the law of reflection is mathematically...
Cut the Knot
Cut the Knot!: Proofs in Mathematics
This site provides an explanation of mathematical proofs. It also has links to different types of proofs.
Varsity Tutors
Varsity Tutors: Hotmath: Practice Problems: Logic and Proof Exercises
Twenty-five problems cover the topic of logic and proof in different geometry settings. They are given with each step to the solution cleverly revealed one at a time. You can work each step of the problem then click the "View Solution"...
Texas Instruments
Texas Instruments: Bring Geometry to Life
In this activity, students use the Geometer's Sketchpad application to construct Euler's Line, Pythagorean Proof, and Fermat's point. They also investigate the concept of perimeter.
McGraw Hill
Glencoe Mathematics: Self Check Quiz on Reasoning & Proof
The online assessment demonstrates knowledge of concepts utilized in Geometry. The multiple choice questions test students on mathematical reasoning and proof.
Maths Challenge
Maths challenge.net: Right Angle Reasoning
A geometry problem for students to use their mathematical reasoning skills to explain a right triangle property.
Other
Math Lab: How to Write a Good Proof
This site offers a brief description and an example of a paragraph proof. And remember, "there is never just one way of stating a proof," so others are mentioned as well.
National Council of Teachers of Mathematics
The Math Forum: Geometry Turned On
This Math Forum site contains many mathematical and geometric explanations and proofs of many different topics that have been done using a geometry software called Geometer's Sketchpad. The explanations are very detailed and clear;...
Khan Academy
Khan Academy: Line and Angle Proofs
Explore different ways of proving some theorems about lines and angles. Some transformations are used. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video, or receive hints.
Math Planet
Math Planet: Geometry: If Then Statement
If-then statements are explained throught the use of examples and a video lesson. [1:16]
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