| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 370 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 - 126 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
...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 - 456 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
...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 - 42 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
...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.... | |
| William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Plane - 1910 - 263 pages
...KF BC+CD + DE + EA _ AB FG + GH+ HJ + JK+ KF FG ' § 363 §335 PROPOSITION XXVI. THEOREM. 376. Two **similar polygons may be divided into the same number of similar triangles,** similarly placed. Given two similar polygons, ABCDE and FGHKL. To prove As ABC, ACD, etc., similar,... | |
| William Herschel Bruce, Claude Carr Cody - Geometry, Solid - 1912 - 110 pages
...homologous altitudes of two similar triangles have the same ratio as any two homologous sides. 376. Two **similar polygons may be divided into the same number of similar triangles,** similarly placed. 391. The square of the x hypotenuse of a right triangle is equal to the sum of the... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 457 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 ABCDE ~ polygon A'B'C'D'E'. To prove A ABC... | |
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