 | William Neville Rose - Mathematics - 1920 - 542 pages
...the equal angles of triangles which are equiangular to one another are proportionals. Euc. VI. 19. Similar triangles are to one another in the duplicate ratio of their homologous (ie, corresponding) sides. Euc. VI. 20. Similar polygons have to one another the duplicate ratio of... | |
 | Trinity College (Dublin, Ireland) - 1921 - 722 pages
...if two triangles have their sides proportional they are equiangular. 5. Show that similar hexagons are to one another in the duplicate ratio of their homologous sides. 6. Construct a figure similar to one figure and equal in area to another. Practical. [Take as unit... | |
 | James Park - Azimuth - 1922 - 598 pages
...problem is to determine the angles at A and B. K ZOO etc. ,L SOOOLC. 90° 90 ffff* M D HG The areas of similar triangles are to one another in the duplicate ratio of their similar sides ; hence, as shown by the construction developed by the dotted lines in fig. 58, AEK :... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...base of a similar triangle is 6 in., find the homologous altitude. PROPOSITION XXIV. THEOREM 313. Two similar polygons may be divided into the same number of similar triangles similar each to each and similarly placed. Given polygon ABCDF ~ polygon A'B'C'D'E'. To prove A ABC... | |
 | William Neville Rose - Mathematics - 1928 - 552 pages
...the equal angles of triangles which are equiangular to one another are proportionals. Euc. VI. 19. Similar triangles are to one another in the duplicate ratio of their homologous (ie, corresponding) sides. Euc. VI. 20. Similar polygons have to one another the duplicate ratio of... | |
 | Great Britain. Scottish Education Dept - 1896 - 642 pages
...of similar triangles, having the same ratio to one another that the polygons have ; and the polygons are to one another in the duplicate ratio of their homologous sides. Describe a polygon which shall be similar to a given polygon, but shall have half its area. 8. Draw... | |
 | Education - 1852 - 576 pages
...circle. 8. It is required to describe a square that shall be equal to a given rectilineal figure. 9. Similar triangles are to one another in the duplicate ratio of their homologous sides. 12. — EXAMINATION PAPER in Mensuration and the Rudiments of Mechanics. April mh, 1852. TIME : ONE... | |
 | University of Durham - 1879 - 158 pages
...eight times either angle at the base. 6. Define similar triangles, duplicate ratio : — Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. 8. Define a conic section, the tangent to a conic section : — If S be the focus, P any point on the... | |
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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
