 | International Correspondence Schools - Civil engineering - 1899 - 798 pages
...angle E, and the angle C to the angle F, the triangles are FIG. 240. similar, and their areas are to each other as the squares of their homologous sides. For example, if BC = 80 feet, EF = 50 feet, and the area of the triangle ABC = 1,600 sq. ft., then 80s : 50' :: 1,600... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...angle of the other, the sides about the third angles are proportional. Proposition 177. Theorem. 213. Similar triangles are to each other as the squares of their homologous sides. Consult Prop. 166, Cor. V. and Prop. 140. Proposition 178. Theorem. 214. Similar polygons are to each... | |
 | Webster Wells - Geometry - 1899 - 450 pages
...intercept, the areas of the figures may be found by §§ 312 and 316. PROP. VII. THEOREM. 319. Two similar triangles are to each other as the squares of their homologous sides. C AD " Given AB and A'B' homologous sides of similar &ABC and A'B'C', respectively. ABC AS To Prove... | |
 | James Howard Gore - Geometry - 1899 - 266 pages
...Multiplying these ratios (by 207), ABC x ABE = ACxAB ABE x ADE ~ AEx AD' PROPOSITION VIII. THEOREM. 262. Two similar triangles are to each other as the squares of their homologous sides. C Let AB and A'B' be homologous sides of the similar triangles ABC and A'B'C'. To prove that A'B'C'... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...intercept, the areas of the figures may be found by §§ 312 and 316. PROP. VII. THEOREM. 319. Two -similar triangles are to each other as the squares of their homologous sides. C D B Given AB and A'B' homologous sides of similar A ABO and A'B' C", respectively. ABC AT? To Prove... | |
 | International Correspondence Schools - Civil engineering - 1899 - 814 pages
...angle E, and the angle C to the angle F, the triangles are FIG. mo. similar, and their areas are to each other as the squares of their homologous sides. For example, if BC = 80 feet, E F— 50 feet, and the area of the triangle ABC — 1,600 sq. ft., then 80' : 50' :: 1,600... | |
 | Arthur Schultze - 1901 - 392 pages
...AA'B'C'. Ex. 826. If A ABC~AA'B'C', &ndZA = Z A', then AB:A'B' = A'C':AC. PROPOSITION XVI. THEOREM 370. Similar triangles are to each other as the squares of their homologous sides. QED Ex. 827. The sides of a triangle are 4, 7, and 8. What are the sides of a similar triangle, whose... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...x BC : GC x HC. Or, A ABC: &DEF=ACx BC : DF x EF. Therefore, etc. PROPOSITION XXVIII. — THEOREM. Similar triangles are to each other as the squares of their homologous sides. Given. — Let ABC and DEF be similar triangles, having the angle A equal to the angle D, the angle... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...to Ex. 826. If A ABC~AA'B'C', andZA = Z A', then AB:A'B' = A'C(: AC. PROPOSITION XVI. THEOREM 370. Similar triangles are to each other as the squares of their homologous sides. AJt J~» Proof. A ABC = ABxAC = AB AC = AB AB AB? A A'B'O A'B' x AC' AB' A'C' A'B' A'B'~ QED Ex. 827.... | |
 | Arthur Schultze - 1901 - 260 pages
...the ratio of A ABC to Ex. 826. If A ABC~&A'B'C', and /LA = Z 4', then PROPOSITION XVI. THEOREM 370. Similar triangles are to each other as the squares of their homologous sides. Hyp. A To prove Proof. c A' AABC~AA'B'C'. A ABC AT? A ABC = A A'B'C' A'B' x A'C ' A'B' " .4'C"" ^'5'... | |
| |
Similar triangles are to each other as the squares of their homologous sides. 
