...into segments proportional to the adjacent sides. 169. Theorem IX. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. 171. Theorem X. (Converse of Theo. IX.) Two similar polygons are composed...

...(prolonged), are equal.] PROPOSITION XXV. THEOREM 542. Tivo polygons are similar if they are composed of the same number of triangles, similar each to each, and similarly placed. Let the A ABC, ADC, DEC, and EFC be similar respectively to the A GHI, GJl, JLI, and LMI, and be similarly...

...therefore similar. PROPOSITION MX. THEOREM 329. If two polygons are similar, they may be separated into the same number of triangles, similar, each to each, and similarly placed. B D £' • D' Given the similar polygons ABCDE and A'B'ffjyW, divided into triangles by the diagonals...

...SIMILAR POLYGONS' PROPOSITION XIX. THEOREM 329. If tico polygons are similar, they may be separated into the same number of triangles , similar, each to each, and similarly placed. ED E1 D' Given the similar polygons ABODE and A'B'C'D'E', divided into triangles by the diagonals AC,...

...perpendicular, each to each, the triangles are similar. 329. // two polygons are similar, they may be separated into the same number of triangles, similar, each to each, and similarly placed. 342. In a right triangle, I. The altitude to 'he hypotenuse is a mean proportional between the segments...

...SIMILAR POLYGONS. PROPOSITION XXV. THEOREM. 365. If two polygons are similar, they are composed of the same number of triangles, similar each to each, and similarly placed. E BC Let the polygons ABCDE and AU'C'DTS' be similar. From two homologous vertices, as E and E', draw...

...demonstration. OD PROPOSITION XXIII. 309. Theorem. CONVERSE OF PROPOSITION XXII. Two similar polygons can be divided into the same number of triangles, similar each to each and similarly placed. GA G' A' Let polygons ABC, etc., and A'B'C', etc., be similar, and let all possible diagonals be drawn...

...find the shortest side of the less. 327. THEOREM. If two polygons are similar, they may be decomposed into the same number of triangles similar each to each and similarly placed. Given : Similar polygons BE and B'E' ' . To Prove : A ABC similar to A A'B'C'; AACD similar to A A'C'D';...

...triangles, similarly placed. Const. Therefore the polygons are similar. "If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar." § 362 MISCELLANEOUS EXERCISES PEOBLEMS OF CONSTRUCTION 777 To divide one...

...A'B' QED PLANE GEOMETRY — BOOK III PROPOSITION XXIV. THEOREM 362 If two polygons are . composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. HYPOTHESIS. The & ABC, ACD, and ADE are similar respectively to the A A'B'C',...