| Great Britain. Education Department. Department of Science and Art - 1908
...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.... | |
| 1879
...beautifully demonstrated in Euclid's Sixth Book, Propositions 19 and 20, that " similar rectilinear figures **are to one another in the duplicate ratio of their homologous sides"** — that is, that these figures — meaning the areas of them— are to one another as the squares... | |
| Trinity College (Dublin, Ireland) - 1919
...Prove that a right-angled triangle may be divided into two triangles each similar to the whole. 7. **Similar triangles are to one another in the duplicate ratio of their** corresponding sides. Practical. 8. Construct a square containing 6 square inches without extracting... | |
| Great Britain. Scottish Education Dept - 1896
...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... | |
| 1852
...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
...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... | |
| Edinburgh Mathematical Society - 1900
...extremes be equal to the square on the mean, the three straight lines are proportional. EUCLID VI. 19. **Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC,** DEFbetwu similar triangles, having the angles at В, С equal to the angles at E, F respectively :... | |
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