...polygons may be divided into the same number of similar triangles, similarly placed. PROP. XIII. Polygons composed of the same number of triangles, similar each to each, and similarly placed, are similar. PROP. XIV. The perimeters of similar polygons are proportional to any homologous lines....

...is similar to AB CDE. Hence we arrive at ihe following useful theorem : — Theorem I. — If tivo polygons are composed of the same number of triangles•...each and similarly placed, the polygons are similar. The converse theorem is also true. State it. If each side of a polygon is 2, 3, 4, etc., times as great...

...similarly placed, the polygons are similar. PROPOSITION VII. Two similar polygons may be decomposed into the same number of 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...

...homologous altitudes of similar triangles equals the ratio of similitude of the triangles. PROPOSITION XIX. If two polygons are composed of the same number of...each and similarly placed, the polygons are similar. PROPOSITION XX. CONVERSE OF PROP. XIX. Two similar polygons may be divided into the same number of...

...and similarly placed, the polygons are similar. Let the polygons AB CD EF and A' B' C' D' E' F' be composed of the same number of triangles, similar each to each and similarly placed, ABC being similar to A' B' C ', and so on for the other triangles. To prove that the polygons are similar....

...inscribed, 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...

...PROPORTIONAL LINES. PROPOSITION XXII. 307. Theorem. // two polygons are composed 0} the same number 0} triangles, similar each to each and similarly placed, the polygons are similar. Let the polygons ABC, etc., and A'B'C', etc., be composed of the same number of triangles, similar each to...

...those mutually parallel or perpendicular. PROPOSITION XVII. THEOREM. 294. Two polygons are similar if composed of the same number of triangles similar each to each and similarly placed. D ~4' Given: In polygons p and P', triangles AED, ADC, ACB, similar to triangles A'E'D', A'D'C', A'C'B',...

...ratio r, which is the ratio of the corresponding sides. 4. Two similar polygons can be divided into the same number of triangles similar each to each, and similarly placed. For 0 and 0' coincide, the figures can be placed having 0 within each, and the triangles A1OB1, A2OB2...

...ratio r, which is the ratio of the corresponding sides. 4. Two similar polygons can be divided into the same number of triangles similar each to each, and similarly placed. For 0 and 0' coincide, the figures can be placed having O within each, and the triangles AiOBi, A2OB2...