...similarity (24). PROPOSITION XI.— THEOREM. 39. Conversely, two similar polygons may be decomposed into lhe same number of triangles similar each to each and similarly placed. Let ABCD, etc., A'B'C'D', etc., be two similar polygons. From two homologous vertices, A and A', let diagonals...

...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...

...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,...

...we can prove that A DBC is similar to A KGH. QED 279. COR. — Two similar polygons can be divided into the same number of triangles similar each to each and similarly placed, by drawing lines to their vertices from any two homologous points. ELEMENTS OF PLANE GEOMETRY. THEOREM...

...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,...

...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, and...

...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...

...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...

...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...

...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',...