| New Brunswick. Board of Education - 1889
...another, are proportionals ; and those which are opposite to the equal angles, are homologous sides. fi. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** T. ALGEBRA. Time, 1 hour SO mitt. Ei-Jiibit the work. 1. Find the value of x in each of the following... | |
| E. J. Brooksmith - 1889
...will touch the circle circumscribing ABC in the point A. 8. Describe a circle about a given square. 9. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 10. In a right-angled triangle if a line be drawn from the right angle perpendicular to the base it... | |
| William Ernest Johnson - 1889 - 504 pagina’s
...product of two lengths. This is equivalent to Euclid's statement that " Similar rectilineal figures **are to one another in the duplicate ratio of their homologous sides."** 24. The area of any rectilineal figure may be found by dividing it into triangles : and applying the... | |
| Royal Military College, Sandhurst - 1890 - 132 pagina’s
...one another, and shall have those angles equal about which the sides are proportionals. 6. Prove that **similar triangles are to one another in the duplicate ratio of their homologous sides.** If ABC be an obtuse-angled triangle, having the obtuse angle BAC; and if AD, AE, be drawn to meet BC... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 515 pagina’s
...OABCD : oabcd :: AOAB : Aoab, ie in dupl. ratio of OA : oa. COR. i. — Similar rectilineal figures **are to one another in the duplicate ratio of their homologous sides.** COR. ii. — If to the homologous sides BC, EF of two similar rectilineal figures P and Q a third proportional... | |
| Thomas Baker - 1891 - 231 pagina’s
...then, the tnanr/ff ABC is to the triangle AED a* the square of AB is to tlte square of AE : that is, **similar triangles are to one another in the duplicate ratio of their homologous sides.** (Euc. VI. 19.) THEOREM VIII. All similar figures are to one another as the squares of then homologous,... | |
| Euclid - 1892 - 518 pagina’s
...Similarly it AB may BH be shewn : CD : DE that Also BA and GH AG HB : DC : FE CF, VI ED; 4. PROPOSITION 19. **THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides.** B Let ABC, DEF be similar triangles, having the i.ABC equal to the L. DEF, and let BC and EF be homologous... | |
| Queensland. Department of Public Instruction - 1892
...LM, and PQ are drawn through O parallel to BC, CA, and AB, show that HK BC LM CA ' AB PQ _ = 2. 7. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 8. Given the base of a triangle, the perpendicular, and the sum of the sides, construct it. !). If... | |
| 1894
...parallel to AD. 4. Similar triangles are to one another in the duplicate ratio of their homologous sides. **Similar triangles are to one another in the duplicate ratio of their** corresponding altitudes. 6. Shew how to solve two equations which contain two unknown quantities when... | |
| Frederick Coate Wade - 1895 - 122 pagina’s
...produced, it will cut them proportionally ; and conversely. Is this converse universally true ? 10. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Bisect a triangle by a line drawn parallel to one of its sides. ALGEBRA. 1. Investigate a rule for... | |
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