If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. Plane Geometry - Page 170by Webster Wells, Walter Wilson Hart - 1915 - 309 pagesFull view - About this book
| George Albert Wentworth - 1889 - 276 pages
...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... | |
| George Albert Wentworth - 1889 - 264 pages
...each to each, and . similarly placed. 155. Theorem. Two polygons are similar if they are divisible **into the same number of triangles, similar each to each, and similarly placed.** 156. Theorem. The perimeters of two similar polygons are proportional to any two homologous sides.... | |
| James Wallace MacDonald - Geometry - 1894 - 76 pages
...are parallel or perpendicular are similar. Proposition V. A Theorem. 210. Two similar polygons may **be divided into the same number of triangles, similar each to each.** Proposition VI. A Theorem. 211. If two polygons can be divided into the same number of triangles, similar... | |
| James Wallace MacDonald - Geometry - 1889 - 80 pages
...are parallel or perpendicular are similar. Proposition V. A Theorem. 210. Two similar polygons may **be divided into the same number of triangles, similar each to each.** Proposition VI. A Theorem. 211. If two polygons can be divided into the same number of triangles, similar... | |
| Edward Albert Bowser - Geometry - 1890 - 414 pages
...hoinohgous 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',... | |
| Edward Albert Bowser - Geometry - 1890 - 420 pages
...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... | |
| Seth Thayer Stewart - Geometry, Modern - 1891 - 422 pages
...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,... | |
| William Chauvenet - 1893 - 340 pages
...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... | |
| George Clinton Shutts - Geometry - 1894 - 412 pages
...Complete the demonstration. PROPOSITION XXIII. 309. Theorem. CONVERSE or PROPOSITION XXII. Two similar **polygons can be divided into the same number of triangles, similar each to each and similarly placed.** GA Let polygons ABC, etc., and A'B'C', etc., be similar, and let all possible diagonals be drawn from... | |
| George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...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... | |
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