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, their third sides will be equal, and their other angles will be equal, each to each. Elements of Geometry and Conic Sections - Page 17by Elias Loomis - 1858 - 234 pagesFull view - About this book
| Adrien Marie Legendre - Geometry - 1874 - 500 pages
...equal to the angle D (Post. 7) ; make AG equal to DE, and draw GC. Tn"en 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... | |
| Benjamin Greenleaf - Geometry - 1874 - 206 pages
...construction, AG is equal to DE ; hence AH is equal to D F. Therefore the two triangles AGH, DE F. Laving 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 (Theo. IV. Bk. I.) But the triangle AGH is similar to ABC; therefore DEF is also... | |
| B. Marks - 1875 - 176 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... | |
| 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 other, each to each, the two triangles will be congruent or symmetrical, and hence equal (15). xxui. If two spherical triangles on the same sphere,... | |
| 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 the... | |
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