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overly detailed proof by cutting out some steps or expand the details of a concise proof sketch, consolidate the proof of a lemma into the main proof, or splice two slightly different proofs together from different sources. We can make up our own examples instead of exactly quoting examples found in a textbook. We can e.g. take a statement written in terms of separate coordinate and rewrite it in terms of vector identities. That type of thing. It's still important to have sources for claims made though, instead of doing
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I'm glad you included a source this time, even if it was the not particularly great source I found for you here. I am nonetheless not impressed with your edit summary of "rv unconstructive", which continues to be gratuitously aggressive. You might consider apologizing to DVdm for your comments, which
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Perhaps we could compromise by replacing two "No"s with a note that, although the most general trapezoids and isosceles trapezoids do not have perpendicular diagonals, there is an infinite number of (non-similar) trapezoids and isosceles trapezoids that do have perpendicular diagonals and are not any
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are the diagonals of the quadrilateral.) if you hunted around in old geometry books. In general, hunting around in books, finding the material that seems most relevant and important, and then adding it with a cited source is a much better strategy for improving
Knowledge than working out identities
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is not that we can include any provable statement, so long as the proof isn't too hard, but rather that we can make statements whose basic claims are established by reliable sources but phrased in ways that aren't necessarily identical. For example, in an article about a theorem, we can simplify an
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I editted them.Could you check if it is right?The area of the
Varignon parallelogram equals half the area of the original quadrilateral. This is true in convex, concave and crossed quadrilaterals provided the area of the latter is defined to be the difference of the areas of the two triangles it is
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Shouldn't the isosceles trapezoid be between the trapezoid and parallelogram instead of between the trapezoid and the rectangle to be fully inclusive? An isosceles trapezoid has one+ pair of parallel sides and one+ pair of congruent sides, so wouldn't that all be inherited by a parallelogram?
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Indeed. Even tangential quadrilaterals which are also right-angled trapezia. (But not every tangential quadrilateral is a trapezium.) You're welcome to extend the diagram to add the new categories, though I think "cyclic right-angled trapezium" might be a bit obscure...
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In general, hunting around in books, finding the material that seems most relevant and important, and then adding it with a cited source is a much better strategy for improving
Knowledge than working out identities for yourself on scrap
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I don't have a clear sense of what's most helpful. Perhaps every "no" has exceptions and could be explained, like "no, becomes a square", etc. With "no, in general" if there's no special name for the special cases!
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The cell for whether an isosceles trapezoid has perpendicular diagonals says "Not in general", but the cell for whether a kite has congruent diagonals, which this same phrase fits equally, says "No". Any thoughts??
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Don't we? When I search Google for the definition of trilateral one of the results is a triangle. Same for trigon. Also, triangle is parallel to a third word for a quadrilateral or tetragon, namely "quadrangle".
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talk about these special case, probably because there's no new symmetry involved. If the articles note the cases, then perhaps a mark in the table could note that with wlink referencing why its noteworthy.
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To answer my own question, an isosceles trapezoid also has congruent diagonals, which a parallelogram does not, so not all properties are inherited. Symmetry is also not inherited. --
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I'm also fairly certain you would be able to find several sources for this claim (For anyone reading along without looking at reverted changes, the identity is: The angle
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Is there a reason why we don't use the word quadragon instead of quadrilateral? After all it has the same meaning as hexagon (hex meaning 6) or pentagon (penta meaning 5)
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Because the word of that form that we (rarely) use is instead "tetragon". I don't know what history led to the different choice of root for the number four. —
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Yes, you are correct. (I'd missed seeing that! Apologies to
Georgia Guy.) The whole table has issues. Have we made it too complicated with the notes?
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David
Eppstein, I have known since I was a child that 'quadrangle' is an alternative name for 'quadrilateral'. Please do not take me for an idiot.
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is to omit the case of convex and concave quadrilateral.)If we check the sign in each case,it is like above.And we have this formura.
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I agree with GG, and changed the "not in general" entry back to "no". Special cases ought to be treated equally. Plus, nothing at
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I think all the other cases are covered by the caveat above the table, but I'll not object if you want to make that adjustment.
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Also, it was explained to you before that sources are not only needed for verification, but also to demonstrate notability. See
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I found in a 1 minute search as used in the proof of "Coolidge's formula". There are many related identities discussed in
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1662:{\displaystyle S={\frac {1}{2}}pq\sin(\theta _{1}\pm \theta _{2})={\frac {a|\sin A|(d-cosD)\pm (d-a\cos A)c|\sin D|}{2}}}
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491:) An isosceles trapezoid can have perpendicular diagonals without being anything other than an isosceles trapezoid.
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David
Eppstein, I was born and bred in the UK and English is my first language. Please don't ever insult me again.
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If you want a language that is designed to be logical and consistent, then
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If you have discovered URLs which were erroneously considered dead by the bot, you can report them with
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If thats the case then why don't we call a triangle a 'trilateral' or a hexagon a 'hexalateral'?
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Just a curious thought more than anything. I am not trying to instigate an edit war or anything.
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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What is a "kite with equal diagonals" called? If the equal diagonals have the same center, its a
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1830:{\displaystyle S={\frac {1}{2}}{\sqrt {p^{2}q^{2}-((d-a\cos A)(d-c\cos D)-ac\sin A\sin D)^{2}}}}
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before doing mass systematic removals. This message is updated dynamically through the template
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Ah yes, the "I don't like this editor so I am going to undo all of their edits for no reason".
1454:{\displaystyle \sin \theta _{1}={\frac {a|\sin A|}{q}},\ cos\theta _{1}={\frac {d-a\cos A}{q}}}
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Again, "hex-" for 6 is a Greek prefix which would not usually be added to a Latin root...
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thanks for the comment. I have added urls for the source, so others can easily verify. -
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A kite can have equal diagonals only when it is a named subset of the set of kites.
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Liking or disliking editors has nothing to do with any of this. This is about
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There could be tangential quadrilaterals which are also trapezoids. No? --
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The angle between diagonals in terms of the sides and diagonals
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http://www.chrisvantienhoven.nl/mathematics/encyclopedia.html
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When you have finished reviewing my changes, please set the
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I disagree because of the caveat I placed above the table.
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Sorry,I misunderstanded a part.It was right about the part.
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template there, but removal also seems fine. The point of
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http://www.cimt.plymouth.ac.uk/resources/topics/art002.pdf
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for additional information. I made the following changes:
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And then it says what routine calculations are. Read it.
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So quadragon (quad meaning 4) should have some sense.
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Routine calculations do not count as original research
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1781:
1778:
1775:
1772:
1769:
1766:
1763:
1760:
1757:
1754:
1751:
1748:
1745:
1742:
1739:
1736:
1731:
1727:
1721:
1717:
1709:
1706:
1701:
1698:
1678:
1656:
1651:
1647:
1644:
1641:
1637:
1633:
1630:
1627:
1624:
1621:
1618:
1615:
1612:
1609:
1606:
1603:
1600:
1597:
1594:
1591:
1588:
1585:
1582:
1578:
1574:
1571:
1568:
1564:
1560:
1554:
1551:
1546:
1542:
1538:
1533:
1529:
1525:
1522:
1519:
1516:
1513:
1508:
1505:
1500:
1497:
1475:
1471:
1448:
1444:
1441:
1438:
1435:
1432:
1429:
1423:
1418:
1414:
1410:
1407:
1404:
1399:
1394:
1389:
1385:
1382:
1379:
1375:
1371:
1365:
1360:
1356:
1352:
1349:
1329:
1326:
1323:
1320:
1317:
1312:
1309:
1304:
1301:
1281:
1259:
1255:
1252:
1249:
1246:
1243:
1240:
1237:
1234:
1231:
1228:
1225:
1222:
1219:
1216:
1213:
1210:
1207:
1204:
1201:
1198:
1195:
1192:
1189:
1186:
1183:
1177:
1174:
1142:
1137:
1134:
1133:
1132:
1131:
1130:
1092:
1091:
1081:David Eppstein
1054:
1053:
1017:
1016:
1015:
1014:
1013:
1012:
1011:
1010:
1009:
1008:
998:David Eppstein
900:David Eppstein
870:
867:
846:
845:
838:
771:
770:
762:Added archive
760:
752:Added archive
750:
742:Added archive
720:
717:
716:
715:
714:
713:
712:
711:
710:
709:
708:
707:
706:
705:
664:
663:
662:
661:
660:
659:
658:
657:
656:
655:
631:
630:
629:
628:
627:
626:
625:
624:
587:
586:
585:
584:
583:
582:
559:
558:
557:
556:
522:
521:
520:
519:
478:
477:
437:
436:Diagonal table
434:
433:
432:
402:
401:
384:
381:
376:
375:
372:
371:
368:
367:
356:
350:
349:
347:
330:the discussion
317:
316:
300:
288:
287:
279:
267:
266:
260:
238:
224:
223:
214:
212:
211:
208:
207:
181:
180:
118:
117:
113:
112:
107:
102:
93:
92:
90:
89:
82:
77:
68:
62:
60:
59:
48:
39:
38:
35:
34:
28:
13:
10:
9:
6:
4:
3:
2:
2378:
2367:
2364:
2362:
2359:
2357:
2354:
2352:
2349:
2347:
2344:
2342:
2339:
2337:
2334:
2332:
2329:
2328:
2326:
2315:
2311:
2307:
2303:
2299:
2293:
2289:
2285:
2279:
2271:
2266:
2265:
2264:
2261:
2258:
2253:
2249:
2248:
2247:
2244:
2241:
2237:
2234:
2230:
2227:
2223:
2219:
2215:
2212:
2211:
2210:
2207:
2204:
2187:
2184:
2181:
2161:
2155:
2152:
2149:
2142:
2138:
2134:
2129:
2125:
2121:
2116:
2112:
2108:
2103:
2099:
2092:
2089:
2086:
2083:
2063:
2055:
2053:
2050:
2047:
2043:
2038:
2031:
2024:
2020:
2010:
2006:
2002:
1998:
1994:
1990:
1986:
1985:
1984:
1981:
1977:
1976:
1975:
1971:
1967:
1963:
1962:
1956:
1952:
1951:
1950:
1949:
1948:
1947:
1939:
1938:
1937:
1934:
1930:
1926:
1923:
1922:
1921:
1917:
1913:
1909:
1905:
1901:
1897:
1896:
1895:
1894:
1891:
1887:
1879:
1875:
1871:
1867:
1863:
1859:
1858:
1853:
1849:
1845:
1841:
1820:
1812:
1809:
1806:
1803:
1800:
1797:
1794:
1791:
1788:
1782:
1779:
1776:
1773:
1770:
1767:
1758:
1755:
1752:
1749:
1746:
1743:
1734:
1729:
1725:
1719:
1715:
1707:
1704:
1699:
1696:
1676:
1654:
1645:
1642:
1639:
1631:
1625:
1622:
1619:
1616:
1613:
1610:
1604:
1598:
1595:
1592:
1589:
1586:
1583:
1572:
1569:
1566:
1558:
1552:
1544:
1540:
1536:
1531:
1527:
1520:
1517:
1514:
1511:
1506:
1503:
1498:
1495:
1473:
1469:
1446:
1442:
1439:
1436:
1433:
1430:
1427:
1421:
1416:
1412:
1408:
1405:
1402:
1397:
1392:
1383:
1380:
1377:
1369:
1363:
1358:
1354:
1350:
1347:
1327:
1324:
1321:
1318:
1315:
1310:
1307:
1302:
1299:
1279:
1257:
1253:
1250:
1247:
1244:
1238:
1235:
1232:
1229:
1226:
1223:
1217:
1211:
1208:
1205:
1202:
1199:
1196:
1190:
1187:
1184:
1181:
1175:
1172:
1164:
1163:
1162:
1161:
1157:
1153:
1149:
1145:
1129:
1125:
1121:
1117:
1116:
1115:
1114:
1113:
1111:
1107:
1103:
1102:77.97.245.229
1099:
1090:
1086:
1082:
1077:
1076:
1075:
1073:
1069:
1065:
1064:77.97.245.229
1061:
1052:
1048:
1044:
1040:
1039:
1038:
1036:
1032:
1028:
1027:77.97.245.229
1024:
1007:
1003:
999:
995:
991:
987:
986:
984:
980:
976:
975:77.97.245.229
972:
966:
965:
960:
959:
954:
953:
952:
951:
950:
946:
942:
938:
934:
930:
926:
922:
918:
917:quadrilateral
914:
911:
910:
909:
905:
901:
897:
896:
895:
893:
889:
885:
884:185.69.145.97
881:
874:
866:
865:
860:
855:
854:
843:
839:
836:
832:
831:
830:
823:
817:
813:
809:
805:
799:
794:
790:
784:
780:
776:
769:
765:
761:
759:
755:
751:
749:
745:
741:
740:
739:
737:
733:
729:
728:Quadrilateral
724:
718:
704:
701:
700:
676:
675:
674:
673:
672:
671:
670:
669:
668:
667:
666:
665:
654:
650:
646:
641:
640:
639:
638:
637:
636:
635:
634:
633:
632:
623:
620:
619:
595:
594:
593:
592:
591:
590:
589:
588:
581:
577:
573:
569:
565:
564:
563:
562:
561:
560:
555:
552:
551:
526:
525:
524:
523:
518:
515:
514:
482:
481:
480:
479:
476:
472:
468:
463:
459:
455:
454:
453:
452:
448:
444:
435:
431:
427:
423:
419:
418:
417:
416:
412:
408:
399:
394:
393:
392:
390:
382:
380:
365:
361:
360:High-priority
355:
352:
351:
348:
331:
327:
323:
322:
314:
308:
303:
301:
298:
294:
293:
289:
285:High‑priority
283:
280:
277:
273:
268:
264:
258:
250:
249:
239:
235:
230:
229:
210:
209:
204:
200:
192:
189:
187:
183:
182:
177:
173:
170:
167:
163:
159:
155:
152:
149:
146:
143:
140:
137:
134:
131:
127:
124:
123:Find sources:
120:
119:
111:
110:Verifiability
108:
106:
103:
101:
98:
97:
96:
87:
83:
81:
78:
76:
72:
69:
67:
64:
63:
57:
53:
52:Learn to edit
49:
46:
41:
40:
37:
36:
32:
26:
25:Quadrilateral
22:
18:
17:
1960:
1957:, called an
1883:
1838:— Preceding
1141:composed of.
1139:
1096:— Preceding
1093:
1058:— Preceding
1055:
1041:He didn't. —
1021:— Preceding
1018:
969:— Preceding
963:
962:
958:trigonometry
957:
956:
941:Double sharp
936:
932:
928:
924:
920:
916:
912:
878:— Preceding
875:
872:
850:
847:
822:source check
801:
795:
782:
778:
774:
772:
725:
722:
679:
598:
530:
493:
439:
403:
386:
379:
359:
319:
263:WikiProjects
246:
198:
184:
171:
165:
157:
150:
144:
138:
132:
122:
94:
19:This is the
1989:wp:policies
789:Sourcecheck
443:Georgia guy
335:Mathematics
326:mathematics
282:Mathematics
148:free images
31:not a forum
2325:Categories
2306:XOR'easter
1902:. And see
859:Report bug
422:Rockychat3
407:Rockychat3
2278:Jacobolus
2257:jacobolus
2240:jacobolus
2203:jacobolus
2046:jacobolus
1904:wp:BURDEN
842:this tool
835:this tool
251:is rated
88:if needed
71:Be polite
21:talk page
2270:Summer92
2252:Summer92
2229:44161807
2023:Summer92
1860:This is
1852:contribs
1840:unsigned
1120:AnonMoos
1098:unsigned
1060:unsigned
1023:unsigned
971:unsigned
929:triangle
925:tetragon
913:-lateral
880:unsigned
848:Cheers.—
645:Tom Ruen
572:Tom Ruen
467:Tom Ruen
199:700 days
186:Archives
56:get help
29:This is
27:article.
2236:3027406
2037:WP:CALC
1925:WP:CALC
1908:WP:CALC
1866:MrOllie
1043:Tamfang
775:checked
732:my edit
362:on the
253:C-class
154:WP refs
142:scholar
2302:paper.
2174:where
1993:wp:AGF
1980:Summer
1933:Summer
1890:Summer
1884:Dear @
1669:(Both
990:Lojban
933:trigon
783:failed
568:square
259:scale.
126:Google
2233:JSTOR
2226:JSTOR
992:, at
240:This
169:JSTOR
130:books
84:Seek
2310:talk
2288:talk
2284:DVdm
2030:fact
2005:talk
2001:DVdm
1970:talk
1966:DVdm
1964:. -
1916:talk
1912:DVdm
1910:. -
1906:and
1886:DVdm
1870:talk
1848:talk
1156:talk
1124:talk
1106:talk
1085:talk
1068:talk
1047:talk
1031:talk
1002:talk
979:talk
945:talk
937:tri-
921:-gon
904:talk
888:talk
779:true
649:talk
576:talk
471:talk
460:nor
447:talk
426:talk
411:talk
354:High
162:FENS
136:news
73:and
2260:(t)
2243:(t)
2218:doi
2206:(t)
2084:cos
2049:(t)
1807:sin
1798:sin
1777:cos
1753:cos
1640:sin
1620:cos
1567:sin
1518:sin
1437:cos
1378:sin
1348:sin
1322:sin
1248:sin
1233:cos
1206:cos
1185:sin
996:. —
931:vs
816:RfC
793:).
781:or
766:to
756:to
746:to
398:Gdr
176:TWL
2327::
2312:)
2290:)
2231:,
2135:−
2122:−
2090:θ
2087:
2064:θ
2033:}}
2027:{{
2007:)
1972:)
1931:.
1918:)
1872:)
1854:)
1850:•
1810:
1801:
1789:−
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1771:−
1756:
1747:−
1735:−
1677:±
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1614:−
1605:±
1587:−
1570:
1541:θ
1537:±
1528:θ
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1440:
1431:−
1413:θ
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1280:θ
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1200:−
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787:{{
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197::
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54:;
2308:(
2286:(
2280::
2276:@
2272::
2268:@
2250:@
2220::
2188:q
2185:,
2182:p
2162:,
2156:q
2153:p
2150:2
2143:2
2139:d
2130:2
2126:b
2117:2
2113:c
2109:+
2104:2
2100:a
2093:=
2021:@
2003:(
1968:(
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1914:(
1868:(
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1813:D
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166:·
158:·
151:·
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128:(
58:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
