 | Francis Joseph Grund - 1830 - 274 páginas
...hypothenuse equals in area the two squares constructed upon the two sides, which include the right angle. 20. The areas of similar triangles are to each other, as the squares constructed upon the sides opposite to the equal angles, and also as the squares upon the heights of... | |
 | Francis Joseph Grund - 1834 - 212 páginas
...query, can you determine the proportion which the areas of similar triangles bear to each other ? A. The areas of similar triangles are to each other as the squares upon the corresponding sides. Q. How can you prove this, for instance, of the two similar triangles... | |
 | Charles Davies - 1840 - 264 páginas
...opposite equal angles 1 Are these sides proportional 1 PLANE GEOMETRY. Properties of Polygons. 13. The areas of similar triangles are to each other as the squares described on their homologous sides. The similar triangles ABC, and DEF, are to each Other, as the... | |
 | 1850 - 488 páginas
...= the distance of the first' perpendicular measured from the acute angle of the triangle ; then as the areas of similar triangles are to each other as the squares of their like sides, we have . , .-. x = 1-732, and the distance of the other perpendicular is in like... | |
 | Evan Wilhelm Evans - 1862 - 116 páginas
...right angle is a mean proportional between the parts of the hypotenuse (Def. 2, Sec. X). THEOREM VIII. The areas of similar triangles are to each other as the squares described on their homologous sides. Let ABC, DEF, be two similar triangles of which the angles A and... | |
 | Eli Todd Tappan - 1864 - 288 páginas
...ietraedrons are to each other as the squares of their edges. This is only a corollary of the theorem that the areas of similar triangles are to each other as the squares of their sides. 641. Corollary — The areas of homologous faces of similar tetraedrons are to each... | |
 | Eli Todd Tappan - 1868 - 432 páginas
...tetraedrons are to each other as the squares of their ed(/es. This is only a corollary of the theorem that the areas of similar triangles are to each other as the squares of their sides. 641. Corollary — The areas of homologous faces of similar tetraedrons are to each... | |
 | Edward Olney - 1872 - 472 páginas
...triangles are to each other as the square roots of their areas. This theorem is involved in the theorem that the areas of similar triangles are to each other as the squares of their homologous sides. It is illustrated in the preceding examples. Ex. Construct a triangle with... | |
 | Eli Todd Tappan - 1873 - 288 páginas
...tetraedrons are to each other as the squares of their edges. This is only a corollary of the theorem that the areas of similar triangles are to each other as the squares of their sides. 641. Corollary. — The areas of homologous faces of similar tetraedrons are to each... | |
 | Edward Olney - 1872 - 270 páginas
...triangles are to each other as the square roots of their areas. This theorem is involved in the theorem that the areas of similar triangles are to each other as the squares of their homologous sides. It is illustrated in the preceding examples. Ex. Construct a triangle with... | |
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... 4. Show that the areas of similar triangles are to each other as the squares of the homologous sides. 
