EngageNY
Proof of the Pythagorean Theorem
What does similarity have to do with the Pythagorean Theorem? The activity steps through the proof of the Pythagorean Theorem by using similar triangles. Next, the teacher leads a discussion of the proof and follows it by an animated...
Shodor Education Foundation
Squaring the Triangle
Teach budding mathematicians how to square a triangle with an interactive that shows a graphical proof of the Pythagorean Theorem. Pupils alter the lengths of the legs using sliders. Using the inputted lengths, the applet displays the...
Mathematics Vision Project
Connecting Algebra and Geometry
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...
Mathematics Vision Project
Similarity and Right Triangle Trigonometry
Starting with similar triangles and dilation factors, this unit quickly and thoroughly progresses into the world of right triangle features and trigonometric relationships. Presented in easy-to-attack modules with copious application...
Mathematics Vision Project
Module 6: Congruence, Construction, and Proof
Trace the links between a variety of math concepts in this far-reaching unit. Ideas that seem very different on the outset (like the distance formula and rigid transformations) come together in very natural and logical ways. This...
EngageNY
Law of Cosines
Build upon the Pythagorean Theorem with the Law of Cosines. The 10th part of a 16-part series introduces the Law of Cosines. Class members use the the geometric representation of the Pythagorean Theorem to develop a proof of the Law of...
Virginia Department of Education
Circles in the Coordinate Plane
Make the connection between the distance formula and the equation of a circle. The teacher presents a lesson on how to use the distance formula to derive the equation of the circle. Pupils transform circles on the coordinate plane and...
EngageNY
Law of Sines
Prove the Law of Sines two ways. The ninth segment in a series of 16 introduces the Law of Sines to help the class find lengths of sides in oblique triangles. Pupils develop a proof of the Law of Sines by drawing an altitude and a second...