tag:blogger.com,1999:blog-38193052.post7186525034369158891..comments2024-03-20T08:57:17.447-03:00Comments on Jornalheiros: Geometria – O Teorema de VivianiPC Filhohttp://www.blogger.com/profile/16547063456626761789noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-38193052.post-57360347651934617032022-05-16T11:15:49.938-03:002022-05-16T11:15:49.938-03:00That's it, Jake!That's it, Jake!PC Filhohttps://www.blogger.com/profile/16547063456626761789noreply@blogger.comtag:blogger.com,1999:blog-38193052.post-66024542177455767062022-05-16T02:12:24.977-03:002022-05-16T02:12:24.977-03:00This one's very simple to prove.
If we draw s...This one's very simple to prove.<br /><br />If we draw segments from P to the vertices of the triangle, such as in the diagram, we make three triangles, the heights of which are s, t, and u and whose bases are all equal in length to the sides of the original triangle. Therefore, we can express the area of the triangle in two ways:<br /><br />A = bh/2<br />A = bs/2 + bt/2 + bu/2 = b(s + t + u)/2<br /><br />Setting the right sides of these two equations equal to each other, we get:<br /><br />bh/2 = b(s + t + u)/2<br />h = s + t + u<br /><br />Therefore, the height of the equilateral triangle is the sum of the heights of the three smaller triangles.jrh150482https://www.blogger.com/profile/10502831081969372299noreply@blogger.comtag:blogger.com,1999:blog-38193052.post-51510125359196120262021-09-19T11:41:33.581-03:002021-09-19T11:41:33.581-03:00O inverso do teorema também é válido.
Se a soma d...O inverso do teorema também é válido.<br /><br />Se a soma das distâncias de um ponto interno de um triângulo aos lados for a mesma independente da localização do ponto, o triângulo é equilátero.PC Filhohttps://www.blogger.com/profile/16547063456626761789noreply@blogger.comtag:blogger.com,1999:blog-38193052.post-67626841537218659232021-09-19T11:26:28.259-03:002021-09-19T11:26:28.259-03:00The converse of the theorem also holds.
If the su...The converse of the theorem also holds.<br /><br />If the sum of the distances from an interior point of a triangle to the sides is independent of the location of the point, the triangle is equilateral.PC Filhohttps://www.blogger.com/profile/16547063456626761789noreply@blogger.com