 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...other as the products of the sides including these angles. Proposition 9. Theorem. 377. The areas of similar triangles are to each other as the squares of their homologous sides. BC Hyp. Let ABC, A'B'C' be similar AS. A ABC BC' To prove __U7 = __t. Proof. Since ZB = / B', (Hyp.)... | |
 | 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... | |
 | 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... | |
 | Rutgers University. College of Agriculture - 1893 - 682 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... | |
 | William Chauvenet - 1893 - 340 pages
...theorems, and the sum of these areas will be the area of the polygon. PROPOSITION VIII.—THEOREM. 19. Similar triangles are to each other as the squares of their homologous sides. Let ABC, A'B'C', be similar triangles ; then ABC A'B'C' Let AD and A'D' be the altitudes; then ABC... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...products of the sides which form the equal angles are also equal, the triangles are equivalent. 253. Theorem. Similar triangles are to each other as the squares of their homologous sides. 254. Theorem. Similar polygons are to each other as the squares of their homologous sides. 255. Problem.... | |
 | 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... | |
 | 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... | |
 | 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?... | |
 | Joe Garner Estill - 1896 - 214 pages
...without a circle, the tangent is a mean proportional between the secant and its external segment. 5. Similar triangles are to each other as the squares of their homologous sides. 6. The diagonals drawn from a vertex of a regular pentagon to the opposite vertices trisect that angle.... | |
| |
Similar triangles are to each other as the squares of their homologous sides. Proof. In the similar .triangles ABC, A'B'C 
