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" The perimeters of two similar polygons have the same ratio as any two corresponding sides. "
Principles of Plane Geometry - Page 44
by James Wallace MacDonald - 1889 - 63 pages
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 426 pages
...perimeters. Denote the perimeter of the first by P, and that of the second by P'. Then £, = ¿|, §295 (the perimeters of two similar polygons have the same ratio as any two homologous sides). But ^ = ^8; §296 B' 0' A' B' BO P . , . . = — Aх. l B' 0' P' Ex. 1. If any two straight lines be...
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Elements of Geometry

George Albert Wentworth - 1881 - 266 pages
...Denote the perimeter of the first by P, and that ~of the second by P'. Then L = AB , § 295 l" A' B' (the perimeters of two similar polygons have the same ratio as any two homologous sides). But 2ÎL = Jfjf. : § 296 B'0' A' B'' * BO P . Ax. 1 Bf 0' P' Ex. 1. If any two straight lines be cut...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 272 pages
...proportional). In like manner we may prove A ECD and E'C'D' similar. QED PROPOSITION XIV. THEOREM. 333. The perimeters of two similar polygons have the same ratio as any two homologous sides. E B c B' C" Let the two similar polygons be ABCDE and A'B'C'D'E', and let P and P' represent their...
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Principles of Plane Geometry

James Wallace MacDonald - Geometry - 1894 - 76 pages
...you can from two similar triangles ; from two similar quadrilaterals ; from two similar pentagons. Proposition IV. A Theorem. 209. Two triangles whose...common point. CASE II. When they are on opposite sides. NOTE. This principle may be used in finding the sides in Proposition VII. Proposition X. A Theorem....
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...number of triangles, similar pair by pair, and similarly placed. 229. Theorem. The perimeters of any two similar polygons have the same ratio as any two homologous sides. a mean proportional between the segments of the hypotenuse. 231. Theorem. A leg of a right triangle...
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Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 390 pages
...similarly placed triangles in P'. .: P and P' may be divided as stated. QED PROPOSITION XIX. THEOREM. 296. The perimeters of two similar polygons have the same ratio as any two homologous sides. Given: AB, A'B', any two homologous sides of two similar polygons, P, P', of which p andp' are the...
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Elements of Geometry: Plane geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...special case. 307. Def. — The perimeter of a polygon is the sum of its PROPOSITION XIII. THEOREM 308. The perimeters of two similar polygons have the same ratio as any two homologous sides. £—'c' »' GIVEN—the perimeters P and P ' of the two polygons ABCDE and A'B'CD'E'. Jr __si tf -o...
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Syllabus of Geometry

George Albert Wentworth - Geometry - 1896 - 68 pages
...they are composed of the same number of triangles, similar each to each, and similarly placed. 333. The perimeters of two similar polygons have the same ratio as any two homologous sides. 334. If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse...
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Elements of Geometry, Part 1

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...case. 307. Def. — The perimeter of a polygon is the sum of its sides. PROPOSITION XIII. THEOREM 308. The perimeters of two similar polygons have the same ratio as any two homologous sides. 'GIVEN— the perimeters P and f of the two polygons ABCDE and A'B'C'D'E'. P AB BC CD TO PROVE _=—-—:...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...307. Def. — The perimeter of a polygon is the sum of it sides. PROPOSITION XIII. THEOREM 308. TIu perimeters of two similar polygons have the same ratio as any two homologous sides. ' GIVEN— the perimeters P and P' of the two polygons ABCDE and A'B'CD'E'. TO PROVE P__A_B__BC_ _CD...
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