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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 - Σελίδα 28
των George Roberts Perkins - 1850 - 320 σελίδες
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Elements of Geometry and Conic Sections

Elias Loomis - 1858 - 234 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...

The Elements of Plane and Solid Geometry

Henry William Watson - 1871 - 285 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...

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

William Chauvenet - 1871 - 368 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...

Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1871 - 58 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...

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

William Chauvenet - 1872 - 368 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...

An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - 1872
...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...

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

William Chauvenet - 1875 - 368 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...

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

Richard Wormell - 1876
...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 ; . - ....

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

Aaron Schuyler - 1876 - 364 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,...

The Register, Cornell University

Cornell University - 1880
...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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