| C. Davies - 1867
...DEB (Ax- 3)In 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 - 320 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.... | |
| Geometry - 1869 - 157 pages
...What do you 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...and the included angle of the other, each to each,** tlie two triangles are equal in all respects. Let the triangles abc and d ef have the side ab of the... | |
| Bernhard Marks - Geometry - 1869 - 157 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... | |
| 1869 - 382 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... | |
| 1870 - 16 pages
...opposite the greater is greater than the angle opposite the less (§76). On the equality of triangles. 12. **When two triangles have two sides and the included angle of the one** respectively equal to two sides and the included angle of the other, the triangles are equal in all... | |
| Bernhard Marks - Geometry - 1871 - 157 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 - 58 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, Adrien Marie Legendre - Geometry - 1872 - 455 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 - 239 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... | |
| |