 | Great Britain. Parliament. House of Commons - 1866 - 862 pagina’s
...equal and parallel to FA. Also that AD, BE, CF, all meet in a point bisecting each other. 11. Show that similar triangles are to one another as the squares of their homologous sides. 12. Show that ever)' solid angle having no re-entering angles is contained by plane angles, which together... | |
 | Rolla Rouse - 1867 - 228 pagina’s
...diameter of including circle . . 68 121 To geometrically find the length of such diameter ...... 69 Similar triangles are to one another as the squares of their homologous or corresponding sides. 122 1. Right angled triangle . . 69 123 2. Acute angled triangle . . .69 124... | |
 | Richard Wormell - 1868 - 286 pagina’s
...triangles, ABC, DBA, DCA, of which one, ABC, is the sum of the other two; since the surfaces of the triangles are to one another as the squares of their homologous sides. We see that if we construct three similar polygons upon the three hypothenuses they will be to one... | |
 | Richard Wormell - 1870 - 304 pagina’s
...triangles, ABC, DBA, DCA, of which one, ABC, is the sum of the other two; since the 'surfaces of the triangles are to one another as the squares of their homologous sides. We see that if we construct three similar polygons upon the three hypothenuses they will be to one... | |
 | Tōkyō Daigaku - 1876 - 180 pagina’s
...= 0 to find the number and situation of the real roots by Sturm's theorem. WE PARSON. GEOMETRY. 1. Similar triangles are to one another as the squares of their homologous sides. 2. An angle formed by a tangent and a chord, is equal to an angle in the opposite segment of the circle.... | |
 | Richard Wormell - 1876 - 268 pagina’s
...triangles, AB С, DBA, DCA, of which one, А В С, is the sum of the other two, since the surfaces of the triangles are to one another as the squares of their homologous sides. Hence, if we construct three similar polygons upon the three hypothenuses, they will be to one another... | |
 | Isaac Sharpless - 1879 - 282 pagina’s
...lines of the polygon ABHG, and prove the resulting polygons similar. Proposition 19. Theorem.—Similar triangles are to one another as the squares of their homologous sides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB : BC :: DE :... | |
 | Isaac Sharpless - 1882 - 286 pagina’s
...the lines of the polygon ABHG, and prove the resulting polygons similar. Proposition 19. Theorem. — Similar triangles are to one another as the squares of their homologous sides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB : BC :: DE :... | |
 | New Jersey. State Board of Education - 1888 - 694 pagina’s
...triangle is produced, the exterior augle is equal to the sum of the two interior opposite angles. 3. Prove that similar triangles are to one another as the squares of their homologous sides ? 4. Prove that in the same circle, or in equal circles, equal chords are equally distant from the... | |
 | 1893 - 1092 pagina’s
...to a given triangle. 11. Triangles having the same altitude are to one another as their bases. 12. Similar triangles are to one another as the squares of their homologous sides. 13. The area of a circle is equal to half the product of the radius and the circumference. 14. Find... | |
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The areas of two similar triangles are to one another as the squares of their homologous or similarly situated sides (fig. 
