 | Elias Loomis - 1858 - 256 σελίδες
...to DF, and join GH. Then the triangles AGH, DEF are equal, since two sides and the included angle in the one, are respectively equal to two sides and the included angle in the other (Prop. VI., BI). But, by hypothesis, AB : DE : : AC B : DF ; therefore AB : AG : : AC... | |
 | Henry William Watson - 1871 - 320 σελίδες
...have seen in Props. 5, 6, and 7, that two triangles are equal in all their parts when — 1 st. Two sides and the included angle of the one are respectively equal to two sides and the included angle of the other ; or 2nd. When two angles and the included side of the one are respectively equal to two... | |
 | William Chauvenet - 1871 - 380 σελίδες
...as to coincide in all their parts. PROPOSITION XX.— THEOREM. 76. Two triangles are equal when two sides and the included angle of the one are respectively equal to two sides and the included angle of the other. In the triangles ABC, DEF, let AB be equal to DE, BC to EF, and the included angle B... | |
 | Elias Loomis - 1871 - 302 σελίδες
...to DF, and join GH. Then the triangles AGH, DEF are equal, since two sides and the included angle in the one, are respectively equal to two sides and the included angle in the other (Prop. VI., BI). But, by hypothesis, AB : DE : : AC B " CE DF; therefore AB : AG : : AC... | |
 | William Chauvenet - 1872 - 382 σελίδες
...as to coincide in all their parts. PROPOSITION XX.— THEOREM. 76. Two triangles are equal when two sides and the included angle of the one are respectively equal to two sides and the included angle of the other. In the triangles ABC, DEF, let AB be equal to DE, BC to EF, and the included angle B... | |
 | Benjamin Peirce - 1872 - 192 σελίδες
...equal angles in the second, are called homologous. 51. Theorem. Two triangles are equal, when two Bides and the included angle of the one are respectively equal to two sides and the included angle of the other. First and Second Cases of Equal Triangles. Place the side DE upon its equal AB. DF will... | |
 | William Chauvenet - 1875 - 390 σελίδες
...their parts. PROPOSITION XX.— THEOREM. 76. Two triangles are equal when two sides and the in-eluded angle of the one are respectively equal to two sides and the included angle of the other. In the triangles ABC, DEF, let AB be equal to DE, BC to EF, and the included angle B... | |
 | Richard Wormell - 1876 - 268 σελίδες
...rect. C R. Join IB, C M. Now AIAB = half rect. AQ, AC AM = half rect. AP; but AIAB = ACAM : For two sides and the included angle of the one are respectively equal to two sides and the included angle of the other ; . • . Rect. AQ = rect. A P. Similarly we may show that Rect. BR = rect. BP ; . - .... | |
 | Aaron Schuyler - 1876 - 384 σελίδες
...parallelogram divides it into two equal triangles. 2. Two parallelograms are equal if two sides and tlie included angle of the one are respectively equal to two sides and the included angle of the other (21, 5). 3. Two rectangles are equal if tliey have equal bases and equal altitudes (83,... | |
 | Cornell University - 1880 - 868 σελίδες
...other as their bases. 3. Two triangles on the same sphere are either equal or symmetrical when two sides and the included angle of the one are respectively equal to two sides and the included angle of the other. 4. A frustum of any cone is equivalent to the sum of three cones whose common altitude... | |
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If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other... 
