 | Edward Brooks - Geometry - 1868 - 284 pages
...and omitting the common factor AHC, we have, or, ABC:DEF::ACXSC:DFXFE. Therefore, etc. THEOREM XVI. Similar triangles are to each other as the squares of their homologous sides. Let ABC and A DE be two similar triangles ; then will they be to each other as the squares of any two... | |
 | Eli Todd Tappan - Geometry - 1868 - 432 pages
...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... | |
 | William Mitchell Gillespie - Surveying - 1869 - 550 pages
...AD is derived from the area of a triangle being equal to its base by half its altitude. (527) Since similar triangles are to each other as the squares of their homologous sides, ABC : DBE : : AB' : BD' ; whence BD = AB J 55? — AB J "* . y ABC ym -f- n The construction of Fig.... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...theorems, and the sum of these areas will be the area of the polygon. PROPOSITION VII.— THEOREM. 20. Similar triangles are to each other as the squares of their homologous sides. Let ABC, A'B'C' be similar tri- •* angles; then, ABC BC2 D' C' DC A'B'C' B'C'* Let AD, A'D', be the... | |
 | Edward Olney - 1872 - 270 pages
...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 one of its sides 2 in length.... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...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 one of its sides 2 in length.... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...rectangle whose adjacent sides are 2 and 3, and then draw a square of the same area. 111. Theorem.— The areas of similar triangles are to each other as the squares of their homologous sides. ILL.— The meaning of this is, that if ABC and DEF are similar, and any side of ABC is 2 times as... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...AB : : AE : AC ; hence (B. H, P. IV.), we have, ADE : ABE : : ABE : ABC ; PROPOSITION XXV. THEOREM. Similar triangles are to each other as the squares of their homologous sides. Let the triangles ABC and DEF be similar, the angle A being equal to the angle D, B to E, and C to... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...equivalent to the sum of the squares El KC and AGHB ; or 28. Corollary. Since To* = TT? + We* iind BC 29. Similar trIangles are to each other as the squares of their homologous sides. Let ABC and D EF be two s similar triangles ; then ABC :DEF—TC2 :DF* Draw BG and E II perpendicular... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...theorems, and the sum of these areas will be the area of the polygon. PROPOSITION VII.— THEOREM. 20. Similar triangles are to each other as the squares of their homologous sides. Let ABC, A'B'C' be similar tri- <« angles ; then, ABC BC* DC A'B'C' B'C" Let AD, A'D', be the altitudes.... | |
| |
Similar triangles are to each other as the squares of their homologous sides. 
