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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... "
Elements of Geometry: With Practical Applications ... - Page 22
by George Roberts Perkins - 1847 - 308 pages
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Elements of Geometry and Conic Sections

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...
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The Elements of Plane and Solid Geometry

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...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

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...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

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...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

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...
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An Elementary Treatise on Plane and Solid Geometry

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...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

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...
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Modern geometry [ed.] with an appendix by W.B. Jack

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 ; . - ....
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Elements of Geometry with Exercises for Students: An an Introduction to ...

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,...
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Cornell University Register and Catalogue

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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