Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Books Books
" FIK are similar ; hence the similar polygons may be divided into the same number of triangles similar each to each, and similarly situated. "
New Elementary Geometry: With Practical Applications : a Shorter Course Upon ... - Page 88
by Benjamin Greenleaf - 1874 - 176 pages
Full view - About this book

New Plane Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 272 pages
...Bid : B 2 C 2 = = r. .-. AiBi + B1C1 + :A 2 B 2 + B 2 C 2 + =r. (Why?) 4. Two similar polygons can be divided into the same number of triangles similar each to each, and similarly placed. For 0 and O" coincide, and the figures can be placed having 0 within each. The triangles AiOBi,...
Full view - About this book

Plane and Solid Geometry

William James Milne - Geometry - 1899 - 398 pages
...Consequently, AD, BE, and CF meet in a point. Why? Proposition XII 309. Draw two polygons such that they may be divided into the same number of triangles, similar, each to each, and similarly situated. How do the homologous angles of these polygons compare in size ? How do the...
Full view - About this book

New Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 416 pages
........ = r. .•. AiBi + BiCi + ..... :A2B2 + J52C2 + ..... =r. (Why?) 4. I wo similar polygons can be divided into the same number of triangles similar each to each, and similarli/ placed. For O and CX coincide, and the figures can be placed having 0 within each. The triangles...
Full view - About this book

The Elements of Plane Geometry

Charles Austin Hobbs - Geometry, Plane - 1899 - 240 pages
...Theorem. 175. If two polygons are similar, the diagonals drawn from homologous vertices divide them into the same number of triangles, similar each to each, and similarly placed. B Hypothesis. ABCDEF and GHKMNO are similar polygons, and from the homologous vertices are...
Full view - About this book

The Essentials of Geometry

Webster Wells - Geometry - 1899 - 424 pages
...proportional. PROP. XXI. THEOREM. 267. (Converse of Prop. XX.) Two similar polygons may be decomposed into the same number of triangles, similar each to each, and similarly placed. A. Given E and E' homologous vertices of similar polygons AC and A'C', and lines EB, EC, E'B',...
Full view - About this book

Syllabus of Propositions in Geometry: Intended for Use in Preparing Students ...

Harvard University - Geometry - 1899 - 39 pages
...sides of the angle. THEOREM VI. 10 Conversely, if two polygons are similar, they can be decomposed into the same number of triangles, similar each to each and similarly placed. THEOREM VII. The perimeters of two similar polygons are in the same ratio as any two corresponding...
Full view - About this book

Plane Geometry

Edward Brooks - 1901 - 278 pages
...DH2 = ~CG2 : FH\ Therefore, A ABC : A DEF => Z<S 2 : UE 2 = UG* : TH\ PROPOSITION XXIX. — THEOREM. Similar polygons may be divided into the same number...of triangles, similar each to each, and similarly placed. Given— Let ,45 CUE and FGHIK be two similar polygons, hav- \ ./' ..-•? ing the angle A...
Full view - About this book

Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - Geometry - 1901 - 460 pages
...on. Why? Why ? CONVERSELY. If the diagonals drawn from one vertex in each of two polygons divide them into the same number of triangles, similar each to each and similarly placed, the two polygons are similar. EXERCISES 1. State the theorem in the first chapter analogous...
Full view - About this book

Mathematics, mechanics, heat

American School (Chicago, Ill.) - Engineering - 1903
...polygons are similar, (article 173.) THEOREM LVII. 180. Conversely, two similar polygons may 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...
Full view - About this book

Plane Geometry

Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...therefore similar. PROPOSITION MX. THEOREM 329. If two polygons are similar, they may be separated into the same number of triangles, similar, each to each, and similarly placed. B D ' • D' Given the similar polygons ABCDE and A'B'ffjyW, divided into triangles by the...
Full view - About this book




  1. My library
  2. Help
  3. Advanced Book Search
  4. Download EPUB
  5. Download PDF