 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...trapezoid is equal to the product of its altitude byhalf 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... | |
 | James Wallace MacDonald - Geometry - 1894 - 76 pages
...construct a parallelogram equivalent to a given square. Proposition XVIII. A Theorem. 253. The areas of similar triangles are to each other as the squares of their homologous sides. See Proposition VII. Proposition XIX. A Theorem. 254. The areas of any similar polygons are proportional... | |
 | James Wallace MacDonald - Geometry - 1889 - 80 pages
...construct a parallelogram equivalent to a given square. Proposition XVIII. A Theorem. 253. The areas of similar triangles are to each other as the squares of their homologous sides. Proposition XIX. A Theorem. 254. The areas of any similar polygons are proportional to the squares... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...equal angles are equal, the triangles are equivalent. EXERCISE. Proposition 9. Theorem. 377. The areas of similar triangles are to each other as the squares of their homologous sides. BCB Of Hyp. Let ABC, A'B'C' be similar As. A ABC BC' To prove _17_ = __,. Proof. Since ZB = Z B', (Hyp.)... | |
 | Education - 1890 - 714 pages
...imagine, 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... | |
 | 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
...by 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... | |
 | 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... | |
| |
Similar triangles are to each other as the squares of their homologous sides. 
