| Elias Loomis - Conic sections - 1858 - 252 pages
...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 - Geometry - 1871 - 316 pages
...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 - Geometry - 1871 - 380 pages
...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 - Geometry - 1871 - 302 pages
...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 - Geometry - 1872 - 382 pages
...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 pages
...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 - Geometry - 1875 - 390 pages
...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 - 264 pages
...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 - Geometry - 1876 - 384 pages
...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 - 864 pages
...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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