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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

## 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,...

## 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...

## 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...

## 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...

## 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',...

## 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...

## 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...

## 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...