...: BC2 : EF2. Therefore similar triangles, etc. PROPOSITION XXVI. THEOREM. Two similar polygons may be divided into the same number of triangles, similar each to each, and similarly situated. Let ABCDE, FGHIK be two similar polygons; they may be divided into the same number of similar...

...Hence, also, ABC : abc = AD- : ad2. SIMILAR POLYGONS. XXVII. • Theorem. Two similar polygons may be divided into the same number of triangles similar each to each. HYPOTII. ABODE and abode are similar polygons, divided into triangles by diagonals drawn from the vertices...

...the angles of a polygon = 180° X the number of bides less two. 4. Two polygons are equal, if they can be divided into the same number of triangles, similar each to each, and similarly placed. 5. A polygon is equilateral, if its sides are equal ; equiangular, if its angles are equal ; regular,...

...polygons ABCDE and FGHKM are similar. (237) QED ELEMENTS OF PLANE GEOMETRY. THEOREM XXI. 278. Two similar polygons can be divided into the same number of triangles similar each to each and similarly placed. Let the polygon ABCDE be similar to the polygon FGHKM, and let diagonals be drawn from the vertices...

...the area of the first than that of the second? An*. 2$. THEOREM IX. Similar polygons may be resolved into the same number of triangles, similar, each to each, and similarly placed. Let P and P' be two similar polygons; then, can they be resolved into the same number of similar triangles,...

...(B. II., P. IV.), we have, ABC : DEF : : ^C* : DF2. PROPOSITION XXVI. THEOREM. Similar polygons may be divided into the same number of triangles, similar, each to each, and similarly placed. Let ABCDE and FGHIK be two similar polygons, the angle A being equal to the angle F, B to G, C to H,...

...of the triangles PROPOSITION XXIV. THEOREM. 283. Two polygons are similar when they are composed of the same number of triangles, similar each to each and similarly placed. In the polygons AE and A'-E', let the triangle ABE be similar to A'B'E', BCE to B'C'E', and CDE to...

...Hence we arrive at the following useful theorem : — Theorem I. — If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. The converse theorem is also true. State it. If each side of a polygon is...

...^. = = = - = = t PROPOSITION VII.—THEOREM. 23. Conversely, two similar polygons may be decomposed into the same number of triangles similar each to each and similarly placed. Let AH CD, etc., A'B'C'D', etc., be two similar polygons. From two homologous vertices, A and A', let...

...sides proportional). PROPOSITION XIII. THEOREM. 332. If two polygons are similar, they are composed of the same number of triangles, similar each to each, and similarly placed. BC B' C Let the polygons ABCDE and A'B'C'D'E' be similar. From two homologous vertices, as E and E',...