 | William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...KF BC+CD + DE + EA _ AB FG + GH+ HJ + JK+ KF FG ' § 363 §335 PROPOSITION XXVI. THEOREM. 376. Two similar polygons may be divided into the same number of similar triangles, similarly placed. Given two similar polygons, ABCDE and FGHKL. To prove As ABC, ACD, etc., similar,... | |
 | Great Britain. Board of Education - Mathematics - 1912 - 632 pages
...divided so that AB:BC::DE:EF; prove that AD, BE, CF will meet in a point or be parallel. 9. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. If one diagonal of a quadrilateral bisects the angle between two of the sides and is a mean proportional... | |
 | William Herschel Bruce, Claude Carr Cody - Geometry, Solid - 1912 - 134 pages
...homologous altitudes of two similar triangles have the same ratio as any two homologous sides. 376. Two similar polygons may be divided into the same number of similar triangles, similarly placed. 391. The square of the x hypotenuse of a right triangle is equal to the sum of the... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...base of a similar triangle is 6 in., find the homologous altitude. PROPOSITION XXIV. THEOREM 313. Two similar polygons may be divided into the same number of similar triangles similar each to each and similarly placed. Given polygon ABCDE ~ polygon A'B'C'D'E'. To prove A ABC... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...base of a similar triangle is 6 in., lind the homologous altitude. PROPOSITION XXIV. THEOREM 313. Two similar polygons may be divided into the same number of similar triangles similar each to each and similarly placed. Given polygon ABCDE ~ polygon A'B'C'D'£'. To prove A ABC... | |
 | Trinity College (Dublin, Ireland) - 1914 - 568 pages
...these equal angles are reciprocally proportional. 6. Prove that similar polygons can be divided up into the same number of similar triangles, having...same ratio to one another that the polygons have. 7. Parallelograms which are equiangular are to one another in the ratio which is compounded of the... | |
 | Industrial arts - 1879 - 670 pages
...beautifully demonstrated in Euclid's Sixth Book, Propositions 19 and 20, that " similar rectilinear figures are to one another in the duplicate ratio of their homologous sides" — that is, that these figures — meaning the areas of them— are to one another as the squares... | |
 | Trinity College (Dublin, Ireland) - 1916 - 554 pages
...of triangles having the same altitude are to one another as their bases. 6. Prove that the areas of similar triangles are to one another in the duplicate ratio of their homologous sides. 7. Show how to construct a triangle equal in area to a given square and similar to a given triangle.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...base of a similar triangle is 6 in., find the homologous altitude. PROPOSITION XXIV. THEOREM 313. Two similar polygons may be divided into the same number of similar triangles similar each to each and similarly placed. Given polygon ABCDE ~ polygon A'B'C'D'£'. To prove A ABC... | |
 | Trinity College (Dublin, Ireland) - 1919 - 562 pages
...Prove that a right-angled triangle may be divided into two triangles each similar to the whole. 7. Similar triangles are to one another in the duplicate ratio of their corresponding sides. Practical. 8. Construct a square containing 6 square inches without extracting... | |
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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
