 | George Albert Wentworth - 1881 - 266 pages
...as any antecedent is to its consequent). That is P : P' : : AB : A' B'. QED GEOMETRY. — BOOK Ш. PROPOSITION XVII. THEOREM. 296. The homologous altitudes...B'O'. We are to prove BO AB B' 0' A' B' In the rt. А B 0 A and B' 0' A', ¿A=¿A' § 278 (being homologous A of the similar А А B С and A' BI СI).... | |
 | George Albert Wentworth - Geometry, Modern - 1882 - 268 pages
...consequents as any antecedent is to its consequent). That is P : P' : : AB : A' B'. GEOMETRY. BOOK ГП. PROPOSITION XVII. THEOREM. 296. The homologous altitudes...similar triangles ABC and A'B'C', let the altitudes be BO and B'O'. We are to prove X' BO AB С-0' "" A' B'' In the rt. AB 0 A and 5' О' Л', Z Л = Z Л'... | |
 | George Albert Wentworth - Geometry, Modern - 1879 - 262 pages
...sum of the consequents ns any antecedent is to its consequent). That is P : P' :: AB • A'B'. QED \ PROPOSITION XVII. THEOREM. 296. The homologous altitudes...triangles have the same ratio as any two homologous sides. C A' In the two similar triangles ABC and A'B'C', let the altitudes be B 0 and B'O'. We are to prove... | |
 | George Albert Wentworth - Geometry - 1888 - 272 pages
...BOOK III. PROPOSITION IX. THEOREM. 328. The homologous altitudes of two similar triangles have tlie same ratio as any two homologous sides. In the two...similar triangles ABC and A'B'C', let the altitudes be CO and C'O'. To prove CO AC AB A'C'~ A'B' Proof. In the rt. A COA and C'O'A', Z .4 - Z A', § 319 (being... | |
 | George Albert Wentworth - Geometry - 1888 - 264 pages
...homologous altitudes of tivo similar triangles have the same ratio as any two homologous sides. 0 B In the two similar triangles ABC and A'B'C', let the altitudes be CO and C'O ' . To prove CO AC AB A'C'~ A'B' Proof. In the rt. A CO A and C'O'A', ZA --- Z A', § 319... | |
 | George Albert Wentworth - Geometry, Analytic - 1889 - 264 pages
...321 (two mutually equiangular A are similar). PLANE GEOMETRY. BOOK III. PROPOSITION IX. THEOREM. 328. The homologous altitudes of two similar triangles have the same ratio as any two homologous sides. A 0 A' 0' In the two similar triangles ABC and A'D'C', let the altitudes be CO and C'0>. To prove CO... | |
 | George Albert Wentworth - Geometry - 1893 - 270 pages
...A'B'C' are similar, § 321 (two mutually equiangular & are similar). PROPOSITION IX. THEOREM. 328. The homologous altitudes of two similar triangles have the same ratio as any two Jtomolo/ou.i sides. A o In the two similar triangles ABC and A'B'C', let the altitudes be CO and C'ff.... | |
 | George Albert Wentworth - Geometry - 1895 - 468 pages
...angles, the third supposition only is admissible. § 138 150 PROPOSITION IX. THEOREM. 328. The hmnologous altitudes of two similar triangles have the same ratio as any two homologous sides. A 0 A! 0' In the two similar triangles ABC and A'B'C', let the altitudes be CO and C'O'. AC AB To prove... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...and so for other sides. NOTE. This is the converse of ths. 8, 10. COROLLARIES. 1. The corresponding altitudes of two similar triangles have the same ratio as any two corresponding sides. Why? 2. The corresponding sides of similar triangles are opposite the equal angles.... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...triangles have their sides respectively parallel, or respectively perpendicular, they are similar. 328. The homologous altitudes of two similar triangles have the same ratio as any two homologous sides. 329. Straight lines drawn through the same point intercept proportional segments upon two parallels.... | |
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The homologous altitudes of two similar triangles have the same ratio as any two homologous sides. In the two similar triangles ABC and A'B'C', let the altitudes be B 0 and B'O'. 
