 | Alan Sanders - Geometry - 1903 - 396 pages
...point of intersection of the common chords (prolonged), are equal.] PROPOSITION XXV. THEOREM 542. Tivo polygons are similar if they are composed of the same...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... | |
 | American School (Chicago, Ill.) - Engineering - 1903 - 390 pages
...similar (Theorem LI.) BG_AB_AC..BC Therefore inerefore, _ THEOREH LVI. 179. Two polygons are similar when they are composed of the same number of triangles, similar each to each and similarly placed. In the polygons A — E and A' — E', the triangle ABE will be similar to A' B' E', BCE to B' C' E',... | |
 | John Alton Avery - Geometry, Modern - 1903 - 136 pages
...the opposite side CB produced at D ; to prove that DB : DC = AB : AC. THEOREM IX 169. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. Hyp. In polygons ABCDE and RSTVW, let A ABC, ACD, and ADE be similar respectively... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...CAB are similar. 156 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... | |
 | Fletcher Durell - Geometry - 1911 - 553 pages
...A'G'D' are similar. Art. 327. PROPOSITION XX. THEOREM (CONVERSE OF PROP. XIX) 330. // two polygons are composed of the same number of triangles, similar, each to each, and similarly placed , the polygons are similar. B D Given the two polygons ABCDE and A'B'C'D'W, In which the A ABC, ACI),... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...327. BOOK III. PLANE GEOMETRY PROPOSITION XX. THEOREM (CONVERSE OF PROP. XIX) 330. // two polygons are composed of the same number of triangles, similar, each to each, and similarly placed, the polygons are similar. E' Given the two polygons ABCDE and A'B'C'D'B', in which the A ABC, ACD,... | |
 | Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...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... | |
 | George Clinton Shutts - 1905 - 260 pages
...lines is divided at the point into two equal parts. PROPOSITION XXII. 307. Theorem. // two polygons are composed of the same number of 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... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...homologous sides proportional." § 349 162 PROPOSITION XXV. THEOREM 363 If two polygons are similar, they are composed of the same number of triangles, similar each to each, and similarly placed. HYPOTHESIS. The polygons ABCDE and A'B'C'D'E' are sinular. CONCLUSION. The & ABC, ACD, and ADE are... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...their homologous sides proportional." § 349 PROPOSITION XXV. THEOREM 363 If two polygons are similar, they are composed of the same number of triangles, similar each to each, and similarly placed. HYPOTHESIS. The polygons ABCDE and A'B'C'D'E' are similar. CONCLUSION. The A ABC, ACD, and ADE are... | |
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If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. 
