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" Similar triangles are to each other as the squares of their homologous sides. "
Elements of Geometry and Trigonometry: With Notes - Page 62
by Adrien Marie Legendre - 1822 - 367 pages
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The Academy: A Journal of Secondary Education, Volume 5

Education - 1890 - 714 pages
...with an exercise in Geometry. He has proven absolutely and beyond all peradventure that the areas of similar triangles are to each other as the squares of their homologous sides. The proposition admits of no debate, and whoever does not accept the conclusion " is not of sound mind...
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The Compass.$A monthly journal for engineers, surveyors ..., Volumes 1-3

Engineering - 1891 - 592 pages
...these tables to practical use is briefly as follows, being based on the proposition that the areas of similar triangles are to each other as the squares of their homologous sides, thus, Area ADB : area Al D1 & = (D €? - (Z?1 Cl) • Example. Let A ef B represent the cross section...
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Report of the Superintendent of Public Instruction

Michigan. Department of Public Instruction - Education - 1892 - 524 pages
...the parallelogram, and hence is the product of its base and altitude. 4. Demonstrate — The areas of similar triangles are to each other as the squares of their homologous sides. 5. Inscribe a circle within a given triangle. Demonstrate. (i. Demonstrate — The sum of the three...
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Elementary Geometry

William Chauvenet - 1893 - 340 pages
...trapezoid is equal to the product of its altitude by half the sum of its parallel bases. PROPOSITION VIII. Similar triangles are to each other as the squares of their homologous sides. PROPOSITION IX. Similar polygons are to each other as the squares of their homologous sides. PROPOSITION...
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Report

Rutgers University. College of Agriculture - 1893 - 680 pages
...twice the product of one of these sides by the projection of the other side upon it. 4. The areas of similar triangles are to each other as the squares of their homologous sides. 5. Find the area of a square inscribed in a circle whose area is 48 feet. 6. If two straight lines...
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...of the trapezoid. 6. Two triangles are similar when they are mutually equiangular. 7. The areas of two similar triangles are to each other as the squares of their homologous sides. 8. If the radius of a circle is 6, what is the area of a segment whose arc is 60° ? (Take TT = 3.1416.)...
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Regents Examination Papers

University of the State of New York. Examination Department - Examinations - 1894 - 412 pages
...part? Find the area of each sector when the angle at the center equals 60°. 10 Prove that the areas of similar triangles are to each other as the squares of their homologous sides. 1 1 Show how to construct a triangle equivalent to a given irregular hexagon. 1 2 Draw a rectangle...
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Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 386 pages
...also under the form : The areas of triangles that have an angle of the PROPOSITION IX. THEOREM. 342. Similar triangles are to each other as the squares of their homologous sides. Given: Similar triangles ABC, A'B'C', having AB:AC = A'B': A'C'; To Prove: Triangle ABC : triangle...
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Concrete Geometry for Beginners

Adelia Roberts Hornbrook - Geometry - 1895 - 222 pages
...numbers that their areas are to each other as 9 to 1. 135. You have shown that the areas of similar right triangles are to each other as the squares of their homologous sides. In the same way show the ratio of the areas of similar rectangles. 136. Are circles similar figures?...
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Numerical Problems in Plane Geometry: With Metric and Logarithmic Tables

Joe Garner Estill - 1896 - 186 pages
...employed. (b) Find the area of the regular circumscribed hexagon of a circle whose radius is 1. 6. Two similar triangles are to each other as the squares of their homologous sides. Bowdoin College, June, 1895. 1. The perpendiculars from the vertices of a triangle to the opposite...
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