Showing that an inscribed angle is half of a central angle that subtends the same arc
Three example problems involving perimeter and area
Right triangles and the Pythagorean Theorem
Figuring out angles at the intersection of two lines
A few more 45-45-90 examples and an introduction to 30-60-90 triangles.
A shape that has an infinite perimeter but finite area
Understanding basic ideas in geometry and how we represent them with symbols
Formal definition of a circle. Tangent and secant lines. Diameters and radii. major and minor arcs
This video is from the Khan Academy subject of Math on the topic of Geometry and it covers Length of an arc that subtends a central angle.
Using the KA virtual protractor to measure angles
How to measure an angle in degrees
This video is from the Khan Academy subject of Math on the topic of Geometry and it covers Measuring segments.
This video is from the Khan Academy subject of Math on the topic of Geometry and it covers Measuring volume as area times length.
This video is from the Khan Academy subject of Math on the topic of Geometry and it covers Measuring volume with unit cubes.
Example involving properties of medians
Showing that the three medians of a triangle divide it into six smaller triangles of equal area. Brief discussion of the centroid as well
SSA special cases including RSH
In this lesson, students will learn that math is important in navigation and engineering. Ancient land and sea navigators started with the most basic of navigation equations (Speed x Time = Distance). Today, navigational satellites use equations that take into account the relative effects of space and time. However, even these high-tech wonders cannot be built without pure and simple math concepts basic geometry and trigonometry that have been used for thousands of years. In this lesson, these basic concepts are discussed and illustrated in the associated activities.
Student groups work with manipulatives—pencils and trays—to maximize various quantities of a system. They work through three linear optimization problems, each with different constraints. After arriving at a solution, they construct mathematical arguments for why their solutions are the best ones before attempting to maximize a different quantity. To conclude, students think of real-world and engineering space optimization examples—a frequently encountered situation in which the limitation is the amount of space available. It is suggested that students conduct this activity before the associated lesson, Linear Programming, although either order is acceptable.
SSS, SAS, ASA and AAS postulates for congruent triangles. Showing AAA is only good for similarity and SSA is good for neither