 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...to its consequent FGH (Theo. X. Bk. II.), or as ~A~Bt is to FG*; hence the areas of similar polygons are to each other as the squares described on their homologous sides. 219. Cor. 1. The perimeters of similar polygons are also to each other as their corresponding diagonals.... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...its consequent FGH(Theo. X. Bk. II.), or as ~AB* is to FG* • hence the areas of similar polygons are to each other as the squares described on their homologous sides. 219. Cor. 1. The perimeters of similar polygons are also to each other as their corresponding diagonals.... | |
 | Benjamin Greenleaf - Geometry - 1875 - 204 pages
...sides containing the equal angles were equivalent, the triangles would be equivalent. THEOREM XIX. 215. Similar triangles are to each other as the squares...homologous sides. Let ABC, DEF be two similar triangles, and let AC, DF be homologous sides; then the triangle ABC will be to the triangle DEF as the square... | |
 | Edward Olney - Geometry - 1883 - 344 pages
...x CB = AD x DB + CD 2 . QED AREAS OF SIMILAR FIGURES. PROPOSITION VII. 408. Theorem.—The areas of similar triangles are to each other as the squares described on their homologous sides. DEMONSTEATION. Then is area ABC area EFG AC" EG 2 AB 2 BC 2 Ef 2 FG 2 From the greatest * angle in... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...angle is a mean proportional between the hypotenuse and the adjacent part. THEOREM XIV. The areas of similar triangles are to each other as the squares...homologous sides. Let ABC, DEF, be two similar triangles of which the angles A and B are respectively equal to the angles D and E. It may be shown that their... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...angle is a mean proportional between the hypotenuse and the adjacent part. THEOREM XIV. The areas of similar triangles are to each other as the squares described on their homologous sides. Let ABC, DBF, be two similar triangles of which the angles A and B are respectively equal to the angles D and... | |
 | Charles Davies - Geometry - 1886 - 352 pages
...polygons, they may be divided into an equal number of similar triangles. THEOREM XXI. Similar polygons are to each other as the squares described on their homologous sides. Let ABCDE and FGN1K, be two similar polygons ; then will they be to each other as the squares described... | |
 | Association for the Improvement of Geometrical Teaching - Euclid's Elements - 1888 - 208 pages
...to twice the area of ABC. THEOR. n. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be two similar triangles, having the sides BC, EF homologous^ then shall the triangle ABC be to the triangle DEF in the duplicate ratio... | |
 | Michigan. Department of Public Instruction - Education - 1895 - 686 pages
...point within a diedral to its faces, is the supplement of the diedral. 6. Demonstrate— The areas of similar triangles are to each other as the squares described on their homologous sides. 7. Demonstrate — À line which bisects any angle of a triangle divides the opposite side into segments... | |
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Two similar triangles are to each other as the squares described on their homologous sides. Let ABC, DEF, be two similar triangles, having the angle A equal to D, and The angle B=E. 
