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 are equal in all respects. Elements of Plane Geometry - Page 48by Thomas Hunter - 1878 - 132 pagesFull view - About this book
| 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 - 394 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,... | |
| Wm. H. H. 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... | |
| T S. Taylor - 1880 - 152 pages
...lines to cut off a part equal to the less. 3. 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 bases shall be equal. NOTE. — When two sides of a triangle have been mentioned, the third side... | |
| |