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Is it true that if a line is parallel to a plane then any plane containing that line is always parallel to the given plane?
No. A line can be contained by many, many planes, Picture this, A rectangle with corners - going clockwise - A, B, C and D is the screen of your computer. This is a plane figure. 1 inch away from it a line runs from A1 to C1. The line is parallel to the plane. Now, take a sheet of paper with corners E, F, G and H, and place corner E at corner A of the screen, and place corner F at corner C of the screen. The Line AI is now 'contained' in the plane EFGH. and EFGH is perpendicular to ABCD.
How can you form six four person teams out of eight players so that in three matches all players will be teamed with everyone in the group at least once?
One possible combination is ABCD v EFGH ABEF v CDGH ABGH v CDEF This has been worked with people staying in pairs. So that at different times AB are partnered with CD, EF and GH and the same applies to the other three pairs. There are many more combinations where constant pairings are not important.
How do you carve a cube to make a square pyramid?
Suppose the top face of the pyramid is ABCD with the square EFGH directly below it.Suppose AC and BD meet at P, the apex of the pyramid.Make a cut with a plane through P which is parallel to AB and goes through EF.Make a cut with a plane through P which is parallel to BC and goes through FG.Make a cut with a plane through P which is parallel to CD and goes through GH.Make a cut with a plane through P which is parallel to DA and goes through HE.The result will be the square-based pyramid PEFGH.
Is it true if a line is parallel to plane it is parallel to any line in the plane?
If your definition of parallel lines is that they never meet, then the answer is yes. If, however, the definition is that they remain equidistant from one another at all points, then, in my opinion, the answer is no. It is difficult to explain the second without recourse to diagrams which are very difficult to manage on this site. So consider a cube with vertices ABCD forming the top face and EFGH (in corresponding order) forming the bottom face. Now AB is parallel to the bottom plane - EFGH. And AB is clearly parallel to EF and any line parallel to EF. But is AB parallel lines such as FG? True, they will never meet but the distance between them increases as you move away from BF - ie they are not the same distance apart. Incidentally, Euclid's parallel postulate was phrased in a very different way from the one most mathematicians come across it. That version is a much later equivalent statement.
How do you find the midpoint of segment gf if the quadrilateral EFGH has coordinates E 2b b F 3b 2b G b 0 and H 0 0?
Each coordinate of the midpoint of a line segment is the average of the correspondingcoordinates of the end points.'x' of the midpoint = average of 'x' of the endpoints'y' of the midpoint = average of 'y' of the endpointsFor segment GF, you only need the coordinates of 'G' and 'F'.G . . . (b, 0)F . . . (3b, 2b)'x' of the midpoint = 1/2 (b + 3b) = 1/2 (4b) = 2b'y' of the midpoint = 1/2 (0 + 2b) = 1/2 (2b) = bCoordinates of the midpoint . . . (2b, b)
Polygons abcd and efgh are similar find the length of CD?
4
If Polygons abcd is similar to efgh are similar find the length of ab?
It is k times the perimeter of eh where k is the constant ratio of the sides of abcd to the corresponding sides of efgh.
If polygons ABCD and EFGH are similar. What is the perimeter of ABCD?
It is k times the perimeter of EFGH where k is the constant ratio of the sides of ABCD to the corresponding sides of EFGH.
Top polygons abcd and efgh are similarfind the length of ab the length of fe is 15 and ab and fe are similar?
12
If Polygons abcd and efgh are similar what is the perimeter of efgh?
It is k times the perimeter of abcd where k is the constant ratio of the sides of efgh to the corresponding sides of abcd.
Polygons abcd and efgh are similar. find the length of eh?
The question cannot be answered without information about the relative sizes of the two polygons.
What is the length of eh if abcd and efgh are similar?
It is the scale factor times the length of ad.
If polygons abcd and efgh are simliar what is the perimeter of abcd?
It is k times the perimeter of efgh, where k is the constant of proportionality between the sides of abcd and the corresponding sides of efgh.
If Abcd efgh are similar find the length of eh?
It is k times the length of Ad where k is the constant of proportionality between the two shapes.
Polygons abcd and efgh are similar. find the perimeter of abcd?
Wonderful! If you had told us something about polygon efgh, and mentioned some small tidbit of information regarding the ratio of similarity, we might have had a fighting chance. The question is a lot like asking: "Bob is older than Jim. How old is Bob ?"
ABCD EFGH Find EF?
2.50
How would you create a file name containing a space?
touch "abcd efgh" touch 'abcd efgh' touch abcd\ efgh are three possibilities, given that you use a Linux shell. Otherwise, it may depend on the specifics of the software (e.g. libreoffice, emacs, firefox...), usually you can do it staghtforwardly when saving a file.
