 | C. Davies - 1867 - 342 pages
...the same manner we may prove that the angle AED ia equal to the angle CEBTHEOREM IV- If two triangles have two sides and the included angle of the one, equal to two sides and ike included angle of the other, each to each, the two triangles will be equalLet the triangles ABC... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...sides of the same square ; and BF equal to BC, for the same reason ; therefore the triangles ABF, HBC have two sides and the included angle of the one equal to two sides and the included angle of the other ; hence they are themselves equal (Prop. Y. Bk. I.). G same altitude BD (Prop. II. Cor.... | |
 | Bernhard Marks - Geometry - 1869 - 172 pages
...think of the areas of the triangles ? d bcef DEMONSTRATION. We wish to prove, that, If two triangles have two sides, and the included angle of the one...and the included angle of the other, each to each, the two triangles are equal in all respects. Let the triangles abc and d ef have the side ab of the... | |
 | Benjamin Greenleaf - 1869 - 516 pages
...construction, AG is equal to DE ; hence AH is equal to D F. Therefore the two triangles AGH, DEF, having two sides and the included angle of the one equal to two...and the included angle of the other, each to each, are themselves equal (Prop. V. Bk. I.). But the triangle AGH is similar to ABC ; therefore DEF is also... | |
 | Bernard Marks - Geometry - 1871 - 172 pages
...the angle ADC. Therefore the angle AB c is equal to the angle ADC. Then the two triangles AB c, AD c, have two sides, and the included angle of the one...and the included angle of the other, each to each, and are equal in all their parts ; that is, the three angles of the one are equal to the three angles... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...because AB is equal to CD, and BC is common to the two triangles <VBC BCD, the two triangles ABC, BCD have two sides and the included angle of the one, equal to two sides and the in. duiled angle of the other ; therefore, the side AC is equa\ to BD (Prop. VI.), and the angle ACB... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...equal to the angle D (Post. 7) ; make AG equal to DE, and draw GC. Then will the triangles AGC and DEF have two sides and the included angle of the one equal...and the included angle of the other, each to each; consequently, GC is equal to EF (PV). Now, the point G may be without the triangle ABC, it may be on... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...and can be applied so as to coincide. PROPOSITION XT. 301. Theorem. — Two parallelograms having two sides and the included angle of the one equal to two...and the included angle of the other, each to each, are equal. DEM.— Let AC and EC be two parallelograms, with AD = EH, AB = EF, and A = E ; then are... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...and can be applied so as to coincide. PROPOSITION XT. 301. Theorem. — Two parallelograms having two sides and the included angle of the one equal to two...and the included angle of the other, each to each, are equal. DEM.— Let AC and EC be two parallelograms, with AD = EH, AB = EF, and A = E ; then are... | |
 | Edward Olney - 1872 - 270 pages
...584, Theorem.—On the same or equal spheres, two spherical triangles having two sides and theincluded angle of the one equal to two sides and the included angle of the other, each to each, are equal, or symmetrical and equivalent. FIG. 337. Fio. &38. DEM.—Let ABC and A'B'C', Fig. 337,... | |
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If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal... 
