This video is from the Khan Academy subject of Math on the topic of Geometry and it covers Determining a translation for a shape.
This text is intended for a brief introductory course in plane geometry. It covers the topics from elementary geometry that are most likely to be required for more advanced mathematics courses. The only prerequisite is a semester of algebra.
The emphasis is on applying basic geometric principles to the numerical solution of problems. For this purpose the number of theorems and definitions is kept small. Proofs are short and intuitive, mostly in the style of those found in a typical trigonometry or precalculus text. There is little attempt to teach theorem-proving or formal methods of reasoning. However the topics are ordered so that they may be taught deductively.
The problems are arranged in pairs so that just the odd-numbered or just the even-numbered can be assigned. For assistance, the student may refer to a large number of completely worked-out examples. Most problems are presented in diagram form so that the difficulty of translating words into pictures is avoided. Many problems require the solution of algebraic equations in a geometric context. These are included to reinforce the student's algebraic and numerical skills, A few of the exercises involve the application of geometry to simple practical problems. These serve primarily to convince the student that what he or she is studying is useful. Historical notes are added where appropriate to give the student a greater appreciation of the subject.
This book is suitable for a course of about 45 semester hours. A shorter course may be devised by skipping proofs, avoiding the more complicated problems and omitting less crucial topics.
Showing that all of the angles of an equilateral triangle are 60 degrees
Three example problems involving isosceles and equilateral triangles. 2 from Art of Problem Solving (by Richard Ruscyk) book
The magic and mystery of the Euler Line
Proving the somewhat mystical result that the circumcenter, centroid and orthocenter
Integrating what we know about isosceles triangles and parallel lines
This video is from the Khan Academy subject of Math on the topic of Geometry and it covers Example using algebra to find measure of complementary angles.
This video is from the Khan Academy subject of Math on the topic of Geometry and it covers Example using algebra to find measure of supplementary angles.
What a medial triangle is and its properties
Working individually or in groups, students explore the concept of stress (compression) through physical experience and math. They discover why it hurts more to poke themselves with mechanical pencil lead than with an eraser. Then they prove why this is so by using the basic equation for stress and applying the concepts to real engineering problems.
Another example of using congruency to figure out a bunch of angles
This video is from the Khan Academy subject of Math on the topic of Geometry and it covers Figuring out angles between transversal and parallel lines.
Example of using similarity and congruence to find the area of a triangle
Using the SSS, ASA, SAS, and AAS postulates to find congruent triangles
This video is from the Khan Academy subject of Math on the topic of Geometry and it covers Finding central angle measure given arc length.
Example of angle hunting!
The resource "Applications of Probability" is a module in the "Coordinate Algebra and Geometry" course. The course is included in the Georgia Virtual Learning resource series available in the open educational resources collection of the NCLOR. This resource is included in the Mathematics discipline with the subject of Geometry.
The resource "Circles and Volume Part One: Angles, Arcs, and Segments" is a module in the "Coordinate Algebra and Geometry" course. The course is included in the Georgia Virtual Learning resource series available in the open educational resources collection of the NCLOR. This resource is included in the Mathematics discipline with the subject of Geometry.
The resource "Circles and Volume Part Two: Arc Length, Sector Area, and Volume" is a module in the "Coordinate Algebra and Geometry" course. The course is included in the Georgia Virtual Learning resource series available in the open educational resources collection of the NCLOR. This resource is included in the Mathematics discipline with the subject of Geometry.