 | Joe Garner Estill - 1896 - 186 pages
...of a circumference of given radius which cuts at right angles a given circumference ? 4. Show that the areas of similar triangles are to each other as the squares of the homologous sides. 5. Prove that the square described upon the altitude of an equilateral triangle... | |
 | George D. Pettee - Geometry, Modern - 1896 - 272 pages
...of a circumference of given radius which cuts at right angles a given circumference ? 4. Show that the areas of similar triangles are to each other as the squares of the homologous sides. , 5. Prove that the square described upon the altitude of an equilateral triangle... | |
 | William Richard King - Mechanical engineering - 1906 - 428 pages
...the center of gravity of the remaining quadrilateral. 276 are to each other in area as 1 : 4. Since the areas of similar triangles are to each other as the squares of homologous sides, we have : A n 1 : 4 = Aff2 : AD2; whence, AG=. Let x denote the distance of the... | |
 | George William Myers - Mathematics - 1910 - 304 pages
...expressed in 4. 6. Show that mc=^2(a'+b2) — c' in any triangle ABC. PROPOSITION VIII 246. Theorem: The areas of similar triangles are to each other as the squares of the homologous sides. Denoting the areas of the given triangles by T and T' (Fig. 277), we have... | |
 | Geometry, Plane - 1911 - 192 pages
...centre of a circumference of given radius which cuts at right angles a given circumference? 4. Show that the areas of similar triangles are to each other as the squares of the homologous sides. 5. Prove that the square described upon the altitude of an equilateral triangle... | |
 | William Richard King - Mechanics, Applied - 1911 - 284 pages
...the median AD. The triangles AEF and ABC are similar, and are to each other in area as 1 : 4. Since the areas of similar triangles are to each other as the squares of homologous sides, we have Let x denote the distance of the required center of gravity of the quadrilateral... | |
 | Julius J. H. Hayn - Geometry, Plane - 1925 - 328 pages
...corresponding sides in the ratio of 2: 3. Prove that their areas are in the ratio of 4:9. 5. Prove that the areas of similar triangles are to each other as the squares of homologous altitudes. 6. In the triangle ABC, the line AE is one-third of AB, and the line AF is... | |
 | Military Academy, West Point - 906 pages
...Theorem: The area of a triangle is equal to (\Vt. 12.) (Complete statement and prove.) (b) Theorem: The areas of similar triangles are to each other as the squares on homologous sides. No. 8.— (a) Define similar polygons. (Wt. 12.) (b) To construct a polygon similar... | |
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Similar triangles are to each other as the squares described on their homologous sides. Let ABC, DEF be two similar triangles... 
