National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Triangle Altitudes
Here at the Math Forum, Dr. Math proves the concurrency of the altitudes of a triangle. Links are provided for associated topics.
Lawrence Hall of Science
The Math Page: Skill in Algebra: The Pythagorean Theorem
Here is a site that clearly and thoroughly explains the Pythagorean Theorem from solving for missing sides of a right triangle through its proof. There are example problems solved, problems for the student to attempt, and answers to the...
Illustrative Mathematics
Illustrative Mathematics: g.co Reflections and Isosceles Triangles
This task has students link their intuitive notions of symmetries of a triangle with statements proving that said triangle is unmoved by applying certain rigid transformations. The mechanism through which students do this is via...
Alabama Learning Exchange
Alex: Growing in a Triangle
Middle school middle schoolers explore the Pythagorean Theorem by measuring and calculating diagonal lengths using the Pythagorean Theorem. Students view an animated proof of the Pythagorean Theorem. They access an Internet site to view...
Cut the Knot
Cut the Knot: Existence of the Orthocenter
This site defines the altitude of a triangle and gives the standard notation for altitudes of a triangle. The site then goes to list several proofs involving altitudes and orthocenters.
University of British Columbia
University of British Columbia: Proof of the Pythagorean Theorem
A geometric model that proves the Pythagorean Theorem in a step-by-step diagram that students can advance at their own pace. Requires Java.
Maths Challenge
Maths challenge.net: Tri Angles
A geometry proof involving exterior angles of a triangle.
Maths Challenge
Maths challenge.net: Maximum Square
A challenging proof like geometry of finding the square inscribed in a triangle.
Cuemath
Cuemath: Angle Bisector Theorem
This short lesson focuses more on the angle bisector theorem. Learn about the angle bisector theorem proof, triangle angle bisector theorem, how to construct angle bisector, and other interesting properties and facts around angle bisectors.
Sophia Learning
Sophia: Cpctc: Lesson 2
This lesson will demonstrate the use of CPCTC in triangle congruencey proofs. It is 2 of 4 in the series titled "CPCTC."
Math Is Fun
Math Is Fun: Triangles Contain 180 Degrees
Students learn about the angle-sum theorem. A definition, example, and proof are included.
Cuemath
Cuemath: Hypotenuse Leg Theorem
Explore the world of the hypotenuse leg theorem in this mini-lesson. Provides a definition, examples, and practice questions with answers that help with understanding their properties.
Maths Challenge
Maths challenge.net: Corner Circle
This is a "three star" geometry problem where prior knowledge of circles and triangles is recommended to solve this circle in the corner problem.
Maths Challenge
Maths challenge.net: Shaded Hexagon
A problem with equilateral triangles and area to solve this "Shaded Hexagon" problem. Mathematical reasoning and triangle knowledge will be needed to solve the problem.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Proving the Existence of the Centroid
At this site you will find the proof of the existence of the centroid for any triangle.
Maths Challenge
Maths challenge.net: Shaded Square
A problem of finding the fraction of a square that is shaded given criterion. Students will have to use their mathematical reasoning and triangle solving skills to solve this area problem.
Wolfram Research
Wolfram Math World: Law of Cosines
This page from MathWorld.com gives a good explanation of the Law of Cosines, which relates the lengths of the legs of a triangle to the angles. This site shows how the formula is derived, along with a triangle to clarify variables. Also...
TED Talks
Ted: Ted Ed: How Many Ways Are There to Prove the Pythagorean Theorem?
Betty Fei details these three famous Pythagorean theorem proofs.
Other
Antonio Gutierrez: Geometry From the Land of the Incas
Discovering the properties of constructions, seeing proofs in action, and viewing problems come to life here with this wonderful use of technology in the classroom. Single steps are explained and illustrated one at a time so that the...
Lawrence Hall of Science
The Math Page: Trigonometry: The Law of Sines
Work through an explanation of the law of sines, how it is used with an obtuse angle, and a proof of the law of sines. Great site for students studying trigonometry.
Alabama Learning Exchange
Alex: The Pythagorean Theorem in the Real World
The introduction of this lesson has students verifying the famous Pythagorean Theorem with a hands-on proof. Students will then apply the Theorem in one of two ways: by solving for the side lengths of a right triangle and by determining...
Oswego City School District
Regents Exam Prep Center: Theorems and Postulates for Geometry
Here is a partial list of theorems, postulates, and properties.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Centroid: Center of Gravity
At this site you will find am online discussion about the centroid of a triangle. The page begins with a discussion of observations leading to the centroid of a triangle. Dr. Math explains the correct findings as well as the errors made...
Varsity Tutors
Varsity Tutors: Hotmath: Algebra Review: Angle Sum Theorem
Find a quick, concise explanation of the Angle Sum Theorem. A step by step explanation of the proof is included to help you understand the theorem.
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