 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...and the lines joining their homologous vertices meet in a point. PROPOSITION XXVI. THEOREM 303. Two similar polygons may be divided into the same number of similar triangles similar each to each and similarly placed. A* E' Hyp. Polygon ABCDE ~ polygon A'B'OD'E'. To prove A... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...and the lines joining their homologous vertices meet in a point. PROPOSITION XXVI. THEOREM 303. Two similar polygons may be divided into the same number of similar triangles similar each to each and similarly placed. >zi A* ^^ E E' Hyp. Polygon ABCDE ~ polygon A'B'C'D'E'.... | |
 | Samuel Bower Sinclair - Education - 1903 - 140 pages
...method of teaching the preposition is superior to the former method is as true as the statement that "similar triangles are to one another in the duplicate ratio of their homologous sides." And yet notwithstanding all this there are many good teachers who are vigorously opposed to all study... | |
 | 1903 - 898 pages
...the special case when AB is one side of an equilateral triangle inscribed in the circle. 8. Show that similar triangles are to one another in the duplicate ratio of their homologous sides. ABC is a triangle. Two circles are drawn, one to touch Alt at A and to pass through C, the other to... | |
 | Euclid - Euclid's Elements - 1904 - 488 pages
...FE jular to the A FD. FE.' ewn that DE. CF, ED. DFE, vI. 4. V. 14. VI. 4. PROPOSITION 19. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. A Let ABC, DEF be similar triangles, having the L ABC equal to the L DEF, and let BC and EF be homologous... | |
 | 1905 - 614 pages
...Describe an isosceles triangle having each of the angles at the base double of the vertical angle. 4. Similar triangles are to one another in the duplicate ratio of their homologous titles. 5. If any similar rectilineal figure be similarly described on the three sides of a right-angled... | |
 | Cora Lenore Williams - Geometry - 1905 - 122 pages
...corresponding sides proportional. ing angles equal and their corresponding sides proportional. Prop. 115. Similar polygons may be divided into the same number of similar triangles. Prop. 116. Polygons similar to the same polygon are similar to each other. Prop. 117. If in a right-angled... | |
 | Great Britain. Education Department. Department of Science and Art - 1908 - 328 pages
...correspond, show that the remaining angles are either equal or supplementary. (30) 44. Show that the areas of similar triangles are to one another in the duplicate ratio of their homologous sides. Show that similar triangles are to each other in the same ratio as the areas of their inscribed circles.... | |
 | Civil Service Commission of Canada - Civil service - 1910 - 240 pages
...whether at the centres or at the circumferences, have the same ratio as the arcs on which they stand. 3. Similar triangles are to one another in the duplicate ratio of their homologous sides. 4. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the... | |
 | Association of Ontario Land Surveyors - Surveying - 1909 - 254 pages
...equilateral and equiangular pentagon in a circle. 8. Inscribe a circle in a given sector ofi a circle. 9. Similar triangles are to one another in the duplicate ratio of their homologous sides. 10. Describe a rectilineal figure which shall be similar to one and equal to another rectilineal figure.... | |
| |
Similar triangles are to one another in the duplicate ratio of their homologous sides. 
