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" Show that the areas of similar triangles are to each other as the squares of the homologous sides. "
Plane Geometry - Page 217
by George D. Pettee - 1896 - 253 pages
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First lessons in Plane Geometry. Together with an application of them to the ...

Francis Joseph Grund - Geometry, Plane - 1830 - 274 pages
...hypothenuse equals in area the two squares constructed upon the two sides, which include the right angle. 20. The areas of similar triangles are to each other, as the squares constructed upon the sides opposite to the equal angles, and also as the squares upon the heights of...
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An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Part 1

Francis Joseph Grund - Geometry, Plane - 1834 - 212 pages
...query, can you determine the proportion which the areas of similar triangles bear to each other ? A. The areas of similar triangles are to each other as the squares upon the corresponding sides. Q. How can you prove this, for instance, of the two similar triangles...
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First Lessons in Geometry: With Practical Applications in Mensuration, and ...

Charles Davies - Geometrical drawing - 1840 - 264 pages
...opposite equal angles 1 Are these sides proportional 1 PLANE GEOMETRY. Properties of Polygons. 13. The areas of similar triangles are to each other as the squares described on their homologous sides. The similar triangles ABC, and DEF, are to each Other, as the...
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The English Journal of Education, Volume 4

Education - 1850 - 488 pages
...= the distance of the first' perpendicular measured from the acute angle of the triangle ; then as the areas of similar triangles are to each other as the squares of their like sides, we have . , .-. x = 1-732, and the distance of the other perpendicular is in like...
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Primary Elements of Plane and Solid Geometry: For Schools and Academies

Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...right angle is a mean proportional between the parts of the hypotenuse (Def. 2, Sec. X). THEOREM VIII. The areas of similar triangles are to each other as the squares described on their homologous sides. Let ABC, DEF, be two similar triangles of which the angles A and...
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Treatise on Plane and Solid Geometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...ietraedrons are to each other as the squares of their edges. This is only a corollary of the theorem that the areas of similar triangles are to each other as the squares of their sides. 641. Corollary — The areas of homologous faces of similar tetraedrons are to each...
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry - 1868 - 432 pages
...tetraedrons are to each other as the squares of their ed(/es. This is only a corollary of the theorem that the areas of similar triangles are to each other as the squares of their sides. 641. Corollary — The areas of homologous faces of similar tetraedrons are to each...
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A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1872 - 472 pages
...triangles are to each other as the square roots of their areas. This theorem is involved in the theorem that the areas of similar triangles are to each other as the squares of their homologous sides. It is illustrated in the preceding examples. Ex. Construct a triangle with...
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A Treatise on Special Or Elementary Geometry

Edward Olney - 1872 - 270 pages
...triangles are to each other as the square roots of their areas. This theorem is involved in the theorem that the areas of similar triangles are to each other as the squares of their homologous sides. It is illustrated in the preceding examples. Ex. Construct a triangle with...
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Treatise on Plane and Solid Geometry for Colleges, Schools, and Private Students

Eli Todd Tappan - Geometry - 1873 - 288 pages
...tetraedrons are to each other as the squares of their edges. This is only a corollary of the theorem that the areas of similar triangles are to each other as the squares of their sides. 641. Corollary. — The areas of homologous faces of similar tetraedrons are to each...
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