Mr. Jones’ Geometry Blog

CHAPTER 12 TEST RETAKE

There will be a retake for the chapter 12 test on Friday, June 8, 2007.
You will not be allowed any extra time, unless you have an IEP that allows you time-and-a-half or double-time. When the bell rings, you are finished.

If you do not take the test on Friday during your regular class time (absent or whyever), I will use your first test score to calculate your grade.

You must remember to bring your calculator–cell phones will not be allowed.

LEARN THE FORMULAS!
See p. 922-923 for all the formulas you will ever need to know.

Spherical Geometry:
Lines on a sphere are actually circles, as they go all the way around the sphere. All lines on a sphere are defined as great circles. Examples of lines on a sphere include the equator and a meridian. Although we might consider the arctic circle to be a line, in spherical geometry it is not.
Any two lines on a sphere intersect two times, and no lines on a sphere are considered to be parallel.
There are an infinite number of lines passing through two points if those two points are the endpoints of a diameter of the sphere, for example the north pole and the south pole.
Triangles on a sphere may be different from triangles on a plane. For example, it is possible to have a triangle on a sphere with not just one or two right angles, but three!

Similar solids
Two solid figures of the same type with equal ratios of corresponding LINEAR measures, such as heights or radii, are called similar solids.
The common ratio is called the SCALE FACTOR of one solid to another.
Two cubes, no matter the size, are similar. The same is true for two spheres.
If two solids are similar, that is the linear measurements have a ratio of a:b, then the corresponding areas have a ratio of a2:b2, and the corresponding volumes have a ratio of a3:b3.
(That’s a-squared to b-squared and a-cubed to b-cubed.)

Make sure you know how to find the length of the leg of a trapezoid using the pythagorean theorem, like question number two on the mid-chapter quiz, as there is a similar problem on the test, since so many people missed it the first time.

Spheres
A sphere is a set of all points in space at a given distance from a point, called the center.
The radius of a sphere is the length (distance) of a segment which extends from the center to the edge.
A chord is a segment with endpoints on the sphere.
A great circle is any circle that divides the sphere into two congruent hemispheres. It passes through the center of the circle.