| B. Marks - 1875 - 176 pages
...What do you think of the areas of the triangles ? a d I cef DEMONSTRATION. We wish to prove, that, // **two triangles have two sides, and the included angle...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... | |
| William Guy Peck - Conic sections - 1876 - 376 pages
...meet at C'. Lay off EA' equal to EA, and draw the arc DA'. The rightangled triangles AED and A'ED, **have two sides and the included angle of the one,...and the included angle of the other, each to each;** hence, they are equal in all their parts; therefore, the angle EA'D is equal to EAD, and the side DA'... | |
| William Guy Peck - Conic sections - 1876 - 412 pages
...draw the arc DA'. The right• angled triangles AED and A 'ED, have two sides and the included atigle **of the one, equal to 'two sides and the included angle of the other, each to each** ; hence, they are equal in all their parts ; therefore, the angle EA'D is equal to EAD, and the side... | |
| Edward Olney - Geometry - 1877 - 272 pages
...form of quadrilateral.] PROPOSITION XV. 301, Theorem,—Two parallelograms having two sides and tin **Included angle of the one equal to two sides 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 they... | |
| Elias Loomis - Conic sections - 1877 - 458 pages
...because AB is equal to CD, and BC is common to the two triangles ABC, BCD, the two triangles ABC, BCD **have two sides and the included angle of the one equal to two sides' and the included angle** of the other; therefore the side AC is equal to BD (Pr. 6), and the angle ACB to the angle CBD. And,... | |
| Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...AF and FE are also equal (const.), and the angles AFC and EFB are equal (Prop. XVII.). Therefore the **two triangles have two sides and the included angle...and the included angle of the other, each to each,** and are every way equal (Prop. IV.); the angle EBF is equal to the angle FCA. But DBG is greater than... | |
| William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...34). xxii. If two spherical triangles on the same sphere, or equal spheres, have tivo sides and th& **included angle of the one equal to two sides and- the included angle of the other, each to each,** the two triangles will be congruent or symmetrical, and hence equal (15). xxui. If two spherical triangles... | |
| Isaac Sharpless - Geometry - 1879 - 282 pages
...required triangle. Proposition 7. Theorem.—If two triangles have two sides and the included angle of **one, equal to two sides and the included angle of the other, each to each,** the triangles will be equal in all their parts. Let ABC, DEF be two triangles which have BA, AC, and... | |
| Elias Loomis - Conic sections - 1880 - 452 pages
...therefore, A and B are mutually equilateral. PROPOSITION XII. THEOREM. If two triangles on equal spheres **have two sides and the included angle of the one equal to two sides and the included** anrjle of the other each to each, their third sides will be equal, and their other angles will be equal... | |
| William Frothingham Bradbury - Geometry - 1880 - 260 pages
...angle DBC—CDB; therefore the whole angle ABC = ADC; therefore the triangles ABC and ADC, having two **sides and the included angle of the one equal to two sides and the included angle** of the other, are equal (80). 89. Scholium. In equal triangles the equal angles are opposite the equal... | |
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