opposite rays geometry example
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From Wikipedia
Cross section (geometry)In geometry, a cross-section is the intersection of a figure in 2-dimensional space with a line, or of a body in 3-dimensional space with a plane, etc. More plainly, when cutting an object into slices one gets many parallel cross-sections.
Cavalieri's principle states that solids with corresponding cross-sections of equal areas have equal volumes.
The cross-sectional area (A') of an object when viewed from a particular angle is the total area of the orthographic projection of the object from that angle. For example, a cylinder of height h and radius r has A' = \pi r^2 when viewed along its central axis, and A' = 2 \pi rh when viewed from an orthogonal direction. A sphere of radius r has A' = \pi r^2 when viewed from any angle. More generically, A' can be calculated by evaluating the following surface integral:
\,\! A' = \iint \limits_\mathrm{top} d\mathbf{A} \cdot \mathbf{\hat{r}},
where \mathbf{\hat{r}} is a unit vector pointing along the viewing direction toward the viewer, d\mathbf{A} is a surface element with outward-pointing normal, and the integral is taken only over the top-most surface, that part of the surface that is "visible" from the perspective of the viewer. For a convex body, each ray through the object from the viewer's perspective crosses just two surfaces. For such objects, the integral may be taken over the entire surface (A) by taking the absolute value of the integrand (so that the "top" and "bottom" of the object do not subtract away, as would be required by the Divergence Theorem applied to the constant vector field \mathbf{\hat{r}}) and dividing by two:
\,\! A' = \frac{1}{2} \iint \limits_A | d\mathbf{A} \cdot \mathbf{\hat{r}}|
From Yahoo Answers
Question:I need to know this for my geometry class. I take a regular geometry course and i need your help! Thanks
Answers:If guess if they are joined then a straight line
Question:It was a quetion that came up to me and a couple of friends.
Answers:You mean TWO OPPOSITE RAYS? like <------------>
Hmm. That's pretty interesting.
As we know Geometry, we can never state a statement if it has no proof, or there is no theorem/postulate that supports it.
I can't recall a theorem in Euclidean Geometry that says: Two opposite rays determine a LINE. But yeah technically speaking, 2 opp. rays determine a line. But I'm no mathematician to claim it. :)
Question:Could you give me some ideas on how these examples of geometry terms are represented in real life? It is supposed to be objects.
Here are the terms.
Point
Line
Segment
Ray
Opposite Rays
Perpendicular Lines
Parrallel Lines
Acute Angle
Obtuse Angle
Right Angle
Vertical Angles (Acute only)
Adjacent Angles (must be less than 180 Degrees)
Linear Pair
Thank you so much !
Answers:You have to put down tile or some type of flooring, you need to be able to use these to figure out how much tile to order and then how to lay this tile so that you have to cut the least amount (I mean really who wants to cut tiles for forever).
Question:A pair of adjacent angles whose noncommon sides are opposite rays
Answers:A linear pair
From Youtube
Rays - YourTeacher.com - Geometry Help :For a complete lesson on geometry rays, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn the definitions of a segment, a ray, and length, as well as the symbols that are used in Geometry to represent each figure. Students also learn the definitions of an endpoint, opposite rays, a coordinate, and a number line. Students are then given geometric figures that are composed of segments and rays, and are asked true false questions about the given figures. Students are also given number lines, and are asked short answer questions about the given number lines. Students are also given the coordinates of the endpoints of segments, and are asked to find the segment lengths.
Euclidean & Non-Euclidean Geometries Part 5: Axioms (Cont.) :Continued from Part 4. I knock a glass candleholder off the shelf during the video, and the sound, while not very loud, might surprise you or your cat. I also knock something else off the ledge, but I don't remember what it was. EUCLID'S POSTULATE III. For every point O and every point A not equal to O there exists a circle with center O and radius OA. DEFINITION. The ray AB is the following set of points lying on the line AB: those points that belong to the segment AB and all points C such that B is between A and C. The ray AB is said to emanate from A and to be part of line AB. DEFINITION. Rays AB and AC are opposite if they are distinct, if they emanate from the same point A, and if they are part of the same line AB = AC. DEFINITION. An "angle with vertex A" is a point A together with two nonopposite rays AB and AC (called the sides of the angel) emanating from A. DEFINITION. If two angles BAD and CAD have a common side AD and the other two sides AB and AC form opposite rays, the angles are supplements of each other, or supplementary angles. DEFINITION. An angle BAD is a right angle if it has a supplementary angle to which it is congruent. EUCLID'S POSTULATE IV. All right angles are congruent to each other. DEFINITION. Two lines m and n are parallel if they do not intersect, ie, if no point lies on both of them. EUCLID'S POSTULATE V. (THE PARALLEL POSTULATE) For every line l (el) and for every point P that does not lie on l (el) there exists and unique line m through P ...