{"id":1553,"date":"2020-08-29T13:58:43","date_gmt":"2020-08-29T11:58:43","guid":{"rendered":"http:\/\/matma.com.pl\/?p=1553"},"modified":"2020-08-29T13:58:43","modified_gmt":"2020-08-29T11:58:43","slug":"czworokaty-4","status":"publish","type":"post","link":"http:\/\/matma.com.pl\/?p=1553","title":{"rendered":"Czworok\u0105ty"},"content":{"rendered":"<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><span style=\"color: #4472c4;\"><strong>Czworok\u0105ty<\/strong>\u00a0<\/span>to figury geometryczne maj\u0105ce cztery boki, cztery k\u0105ty i cztery wierzcho\u0142ki. Ka\u017cdy czworok\u0105t ma dwie przek\u0105tne.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Suma miar k\u0105t\u00f3w w czworok\u0105cie jest r\u00f3wna\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?360^{\\circ&amp;space;}\" alt=\"360^{\\circ }\" align=\"absmiddle\" \/>.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"wp-image-1244 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/czworok%C4%85t11-300x236.png\" sizes=\"(max-width: 234px) 100vw, 234px\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/czworok\u0105t11-300x236.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/czworok\u0105t11.png 365w\" alt=\"\" width=\"234\" height=\"184\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Czworok\u0105ty, kt\u00f3re do tej pory poznali\u015bcie to kwadraty, prostok\u0105ty, r\u00f3wnoleg\u0142oboki, romby, trapezy i deltoidy.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Przypomnijmy kilka wa\u017cnych informacji dotycz\u0105ce tych figur p\u0142askich.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><span style=\"color: #4472c4;\"><strong>Prostok\u0105t<\/strong><\/span>\u00a0to czworok\u0105t, kt\u00f3ry ma dwie pary bok\u00f3w r\u00f3wnoleg\u0142ych i wszystkie jego k\u0105ty wewn\u0119trzne s\u0105 proste. Przek\u0105tne prostok\u0105t\u00f3w s\u0105 takiej samej d\u0142ugo\u015bci i dziel\u0105 si\u0119 na po\u0142owy.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\" wp-image-1427 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/prostok%C4%85t-opissy.png\" alt=\"\" width=\"162\" height=\"116\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">D\u0142ugo\u015bci bok\u00f3w a i b to wymiary prostok\u0105ta.<\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #4472c4; font-family: 'book antiqua', palatino, serif;\"><strong>Pole prostok\u0105ta<\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"wp-image-1252 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/prostok%C4%85t-polee.png\" alt=\"\" width=\"226\" height=\"164\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><span style=\"color: #4472c4;\"><strong>Kwadrat<\/strong>\u00a0<\/span>do czworok\u0105t, kt\u00f3ry ma dwie pary bok\u00f3w r\u00f3wnoleg\u0142ych. Wszystkie boki s\u0105 takiej samej d\u0142ugo\u015bci i wszystkie jego k\u0105ty wewn\u0119trzne s\u0105 proste. Przek\u0105tne kwadratu przecinaj\u0105 si\u0119 w po\u0142owie, pod k\u0105tem prostym i dziel\u0105 k\u0105ty wewn\u0119trzne kwadratu na po\u0142owy (czyli po\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?45^{\\circ&amp;space;}\" alt=\"45^{\\circ }\" align=\"absmiddle\" \/>).<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1428 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/kwadrat-opisssy.png\" alt=\"\" width=\"131\" height=\"138\" \/><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #4472c4; font-family: 'book antiqua', palatino, serif;\"><strong>Pole kwadratu<\/strong><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1253\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/kwadrat-pole.png\" alt=\"\" width=\"168\" height=\"192\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1254\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/kwadrat-polee.png\" alt=\"\" width=\"141\" height=\"184\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><span style=\"color: #4472c4;\"><strong>R\u00f3wnoleg\u0142obok<\/strong><\/span>\u00a0to czworok\u0105t, kt\u00f3ry ma dwie pary bok\u00f3w r\u00f3wnoleg\u0142ych. Przek\u0105tne r\u00f3wnoleg\u0142obok\u00f3w przecinaj\u0105 si\u0119 w po\u0142owie. K\u0105ty le\u017c\u0105ce na przeciw siebie s\u0105 r\u00f3wne.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-915 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/k%C4%85ty-r%C3%B3wnoleg%C5%82obok-300x214.png\" sizes=\"(max-width: 272px) 100vw, 272px\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/k\u0105ty-r\u00f3wnoleg\u0142obok-300x214.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/k\u0105ty-r\u00f3wnoleg\u0142obok.png 515w\" alt=\"\" width=\"272\" height=\"194\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Suma miar k\u0105t\u00f3w przy jednym boku jest r\u00f3wna\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?180^{\\circ&amp;space;}\" alt=\"180^{\\circ }\" align=\"absmiddle\" \/>.\u00a0Jedna przek\u0105tna r\u00f3wnoleg\u0142oboku dzieli go na dwa takie same tr\u00f3jk\u0105ty.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1429 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/r%C3%B3wnoleg%C5%82obok-opissy-300x162.png\" sizes=\"(max-width: 226px) 100vw, 226px\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/r\u00f3wnoleg\u0142obok-opissy-300x162.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/r\u00f3wnoleg\u0142obok-opissy.png 381w\" alt=\"\" width=\"226\" height=\"122\" \/><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #4472c4; font-family: 'book antiqua', palatino, serif;\"><strong>Pole r\u00f3wnoleg\u0142oboku<\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1255 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/r%C3%B3wnoleg%C5%82obok-polee-300x120.png\" sizes=\"(max-width: 350px) 100vw, 350px\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/r\u00f3wnoleg\u0142obok-polee-300x120.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/r\u00f3wnoleg\u0142obok-polee.png 467w\" alt=\"\" width=\"350\" height=\"140\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><span style=\"color: #4472c4;\"><strong>Romb<\/strong><\/span>\u00a0to czworok\u0105t, kt\u00f3ry ma dwie pary bok\u00f3w r\u00f3wnoleg\u0142ych i wszystkie jego boki s\u0105 r\u00f3wne. Przek\u0105tne rombu przecinaj\u0105 si\u0119 w po\u0142owie, pod k\u0105tem prostym.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1433 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/romb-opissy-300x224.png\" sizes=\"(max-width: 181px) 100vw, 181px\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/romb-opissy-300x224.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/romb-opissy.png 344w\" alt=\"\" width=\"181\" height=\"135\" \/><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #4472c4; font-family: 'book antiqua', palatino, serif;\"><strong>Pole rombu<\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1256 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/romb-polee.png\" alt=\"\" width=\"200\" height=\"179\" \/><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1257 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/romb-polee1.png\" alt=\"\" width=\"212\" height=\"200\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><span style=\"color: #4472c4;\"><strong>Trapez<\/strong><\/span>\u00a0to czworok\u0105t, kt\u00f3ry ma przynajmniej jedna par\u0119 bok\u00f3w r\u00f3wnoleg\u0142ych, zwanych podstawami oraz dwa boki, zwane ramionami.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-912 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/trapezz-300x218.png\" sizes=\"(max-width: 213px) 100vw, 213px\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/trapezz-300x218.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/trapezz.png 399w\" alt=\"\" width=\"213\" height=\"155\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Suma miar k\u0105t\u00f3w le\u017c\u0105cych przy ka\u017cdym boku jest r\u00f3wna\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?180^{\\circ&amp;space;}\" alt=\"180^{\\circ }\" align=\"absmiddle\" \/>. W ka\u017cdym trapezie mamy dwie przek\u0105tne.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1436 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/przek%C4%85tne-trapezu-300x201.png\" sizes=\"(max-width: 171px) 100vw, 171px\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/przek\u0105tne-trapezu-300x201.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/przek\u0105tne-trapezu.png 355w\" alt=\"\" width=\"171\" height=\"115\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Wyr\u00f3\u017cniamy trapezy:<\/span><\/p>\n<ul>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">r\u00f3\u017cnoboczne\u00a0\u2013 wszystkie boki s\u0105 r\u00f3\u017cnej d\u0142ugo\u015bci;<\/span><\/li>\n<\/ul>\n<ul>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">r\u00f3wnoramienne\u00a0\u2013 ramiona s\u0105 tej samej d\u0142ugo\u015bci;<\/span><\/li>\n<\/ul>\n<ul>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">prostok\u0105tne\u00a0\u2013 jedno rami\u0119 jest prostopad\u0142e do obu podstaw.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Suma k\u0105t\u00f3w przy ka\u017cdym boku trapezu jest r\u00f3wna\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?180^{\\circ&amp;space;}\" alt=\"180^{\\circ }\" align=\"absmiddle\" \/>.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-916 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/katy-trapez-300x266.png\" sizes=\"(max-width: 270px) 100vw, 270px\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/katy-trapez-300x266.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/katy-trapez.png 429w\" alt=\"\" width=\"270\" height=\"239\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Natomiast w trapezie r\u00f3wnoramiennym k\u0105ty, kt\u00f3re le\u017c\u0105 przy tej samej podstawie s\u0105 sobie r\u00f3wne.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-917 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/kattrapr%C3%B3wn.png\" alt=\"\" width=\"174\" height=\"137\" \/><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #4472c4; font-family: 'book antiqua', palatino, serif;\"><strong>Pole trapezu<\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1259 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/trapez-pole-300x150.png\" sizes=\"(max-width: 320px) 100vw, 320px\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/trapez-pole-300x150.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/trapez-pole.png 483w\" alt=\"\" width=\"320\" height=\"160\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><span style=\"color: #4472c4;\"><strong>Deltoid<\/strong><\/span>\u00a0to czworok\u0105t, kt\u00f3ry ma dwie pary s\u0105siednich bok\u00f3w takiej samej d\u0142ugo\u015bci i \u017cadne boki nie s\u0105 r\u00f3wnoleg\u0142e. Przek\u0105tne deltoidu przecinaj\u0105 si\u0119 pod k\u0105tem prostym. Deltoid wygl\u0105da jak latawiec.\u00a0<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1437 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/deltoid-134x300.png\" sizes=\"(max-width: 167px) 100vw, 167px\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/deltoid-134x300.png 134w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/deltoid.png 274w\" alt=\"\" width=\"167\" height=\"374\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">\u00a0 \u00a0\u00a0<\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #4472c4; font-family: 'book antiqua', palatino, serif;\"><strong>Pole deltoidu<\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-1452 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-deltoidu-201x300.png\" alt=\"\" width=\"215\" height=\"319\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">KWADRAT JEST PROSTOK\u0104TEM!<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">PROSTOK\u0104T JEST R\u00d3WNOLEG\u0141OBOKIEM!<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">ROMB JEST R\u00d3WNOLEG\u0141OBOKIEM!<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">R\u00d3WNOLEG\u0141OBOK JEST TRAPEZEM!<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><span style=\"color: #4472c4;\"><strong>Wielok\u0105t foremny<\/strong><\/span>\u00a0to figura, kt\u00f3ra ma wszystkie boki takiej samej d\u0142ugo\u015bci i wszystkie k\u0105ty o takiej samej mierze.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Przyk\u0142ady wielok\u0105t\u00f3w foremnych:<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1444 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/wielok%C4%85ty-foremne-przyk%C5%82ad-300x224.png\" sizes=\"(max-width: 589px) 100vw, 589px\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/wielok\u0105ty-foremne-przyk\u0142ad-300x224.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/wielok\u0105ty-foremne-przyk\u0142ad-768x574.png 768w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/wielok\u0105ty-foremne-przyk\u0142ad.png 799w\" alt=\"\" width=\"589\" height=\"440\" \/><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Czworok\u0105ty\u00a0to figury geometryczne maj\u0105ce cztery boki, cztery k\u0105ty i cztery wierzcho\u0142ki. Ka\u017cdy czworok\u0105t ma dwie przek\u0105tne. Suma miar k\u0105t\u00f3w w czworok\u0105cie jest r\u00f3wna\u00a0. Czworok\u0105ty, kt\u00f3re do tej pory poznali\u015bcie to kwadraty, prostok\u0105ty, r\u00f3wnoleg\u0142oboki, romby, trapezy i deltoidy. Przypomnijmy kilka wa\u017cnych informacji dotycz\u0105ce tych figur p\u0142askich. Prostok\u0105t\u00a0to czworok\u0105t, kt\u00f3ry ma dwie pary bok\u00f3w r\u00f3wnoleg\u0142ych i wszystkie [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,15],"tags":[],"class_list":["post-1553","post","type-post","status-publish","format-standard","hentry","category-baza-wiedzy","category-klasa-viii"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Czworok\u0105ty - Matma.com.pl<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/matma.com.pl\/?p=1553\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Czworok\u0105ty - Matma.com.pl\" \/>\n<meta property=\"og:description\" content=\"Czworok\u0105ty\u00a0to figury geometryczne maj\u0105ce cztery boki, cztery k\u0105ty i cztery wierzcho\u0142ki. Ka\u017cdy czworok\u0105t ma dwie przek\u0105tne. Suma miar k\u0105t\u00f3w w czworok\u0105cie jest r\u00f3wna\u00a0. Czworok\u0105ty, kt\u00f3re do tej pory poznali\u015bcie to kwadraty, prostok\u0105ty, r\u00f3wnoleg\u0142oboki, romby, trapezy i deltoidy. Przypomnijmy kilka wa\u017cnych informacji dotycz\u0105ce tych figur p\u0142askich. 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