...of triangles, similar each to each. Proposition VI. A Theorem. 211. If two polygons can be divided into the same number of triangles, similar each to each, and similarly placed, the two polygons are similar. Proposition VII. A Problem. 212. A polygon being given, on a line corresponding...

...homologous angles, vertices, sides, and diagonals. 154. Theorem. Two similar polygons are divisible into the same number of triangles, similar each to each, and similarly placed. 155. Theorem. Two polygons are similar if they are divisible into the same number of triangles, similar...

...of triangles, similar each to each. Proposition VI. A Theorem. 211. If two polygons can be divided into the same number of triangles, similar each to each, and similarly placed, the two polygons are similar. Proposition VII. A Problem. 212. A polygon being given, on a line corresponding...

...sides PLANE GEOMETRY. Proposition 22. Theorem. 321. Conversely, two similar polygons may be divided into the same number of triangles, similar each to each, and similarly placed. . Hyp. Let AB0DE, A'B'C'D'E' be two similar polygons divided into AS by the diagonals AC, AD, A'C',...

...and DE = 5, find B'D', D'E', and AE'. Proposition 21 . Theorem. 320. If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. Hyp. Let the As ABC, ACD, ADE of the polygon ABCDE be similar respectively...

...Conclusion : AB 0 and GHJ being any similar, etc. PROPOSITION XIII. 4O4. Theorem : Polygons composed of the same number of triangles, similar each to each, and similarly placed, are similar. Statement: Let any polygons, ABK and FSI, contain the same number of triangles, /, 2,...

...of triangles, similar each to each and similarly placed, the polygons are similar. PROPOSITION VII. Two similar polygons may be decomposed into the same...triangles, similar each to each and similarly placed. PROPOSITION VIII. PROPOSITION IX. If a perpendicular is drawn from the vertex of the right angle to...

...= -^, etc. PROPOSITION XXIV. THEOREM. 267. (Converse of Prop. XXIII.) Two similar polygo>is mni/be decomposed into the same number of triangles, similar each to each, and similarly placed. Let E and E' be homologous vertices of the similar polygons A — E and A' - E', and draw EB, EC, E'B',...

...the polygons are similar. PROPOSITION XX. CONVERSE OF PROP. XIX. Two similar polygons may be divided into the same number of triangles, similar each to each, and similarly placed. PROPOSITION XXI. The ratio of the perimeters of two similar polygons equals the ratio of similitude...

...escribed, and circumscribed circles of any triangle. 3. (a) Two polygons are similar when composed of the same number of triangles, similar each to each, and similarly placed. 4. In the triangle whose sides are a, b, and c, determine the segments of each side made by the bisector...