|Corollary 2||The volume of a cone with a base radius of length r and an altitude of length h is 1/3P r^2h.|
|Theorem 14.10||The volume of a sphere with radius of length r is 4/3Pr^3.|
|Theorem 14.11||The area of a sphere is 4Pr^2.|
|Theorem 14.12||The distance between points P(x1, y1, z1) and Q(x2, y2, z2) is given by the formula d = Ö(x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2.|
|Theorem 15.1||A reflection is an isometry.|
|Theorem 15.2||A translation is an isometry.|
|Theorem 15.3||The resultant image determined by two successive reflections about parallel lines is a translation.|
|Theorem 15.4||A rotation is an isometry.|
|Theorem 15.5||The measure of the angle of rotation formed by two successive reflections (or by the product of two reflections) is twice the measure of the non-obtuse angle between the two lines of symmetry.|
|Theorem 15.6||The transformation defined by adding a constant to the coordinates of each point is a translation.|
|Theorem 15.7||The transformation defined by multiplying each coordinate of each point by a constant is a dilation.|
Note: The concepts in this collection may
not be entirely accurate.
They are for reference only.