 | Isaac Stone - Educational tests and measurements - 1869 - 278 pages
...diagonals of any parallelogram mntually bisect each other. 212. Any two triangles having two angles and the included side of the one equal to two angles and the included side of the other, each to each, arc equal. 213. A triangle is equivalent to half a parallelogram of equal base and altitude.... | |
 | Charles Davies - Geometry - 1870 - 392 pages
...applied the one to the other, the equal parts will coincide. THEOREM v. If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal. Let the two triangles ABC and DEF have the angle A equal... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...if two triangles, &c. PROPOSITION XIV. THEOREM. If two triangles on equal spheres have two angles, and the included side of the one, equal to two angles and the included side of the other, each to each, their third angles will be equal and their other sides will be equal, each to each. If... | |
 | Bernard Marks - Geometry - 1871 - 172 pages
...upon the line ab? » ce / DEMONSTRATION. We wish to prove that, //' tiro triangles have two angles, and the included side of the one equal to two angles and the included side of the other, each to each, the two triangles are equal to each other in all respects. Let the triangles abc and... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...pa1ls (I., D. 14) ; which was to be proved. PROPOSITION VI. THEOREM. If two tria11gles have two angles and the included side of the one equal to two angles and the included side of the other, each to each, the triangles mill be equal in all their parts. In the triangles ABC and DEF, let the... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...XDL 586. Theorem. — On the same, or on equal spheres, two spher-'cal triangles having two angles and the included side of the one equal to two angles and the included side of the other, each to each, are equal, or symmetrical and equivalent. I IKM — Using the same triangles aa in the... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...XIX. 386. Theorem. — On the same, or on equal spheres, two spherical triangles having two angles and the included side of the one equal to two angles and the included side of the other, each to each, are equal, or symmetrical and equivalent. DEM. — Using the same triangles as in the... | |
 | Edward Olney - 1872 - 270 pages
...Then b'c' = be, and Ac' = ac, since the triangles aba and A&V have two angles and the included side of one equal to two angles and the included side of the other. In like manner draw c'd' making angle b'c'd' — bed, c'd'— ed, and Ad'= ad. So, also, making angle... | |
 | Aaron Schuyler - Measurement - 1873 - 508 pages
...the angle COR', since each is a right angle. Hence, the two triangles COR and COR' have two angles, and the included side of the one equal to two angles and the included side of the other, each to each, and are therefore equal in all their parts. Hence, OR, opposite the angle OCR, is equal... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...parts (I., D. 14) ; which was to be proved. PROPOSITION VI. THEOREM. If two triangles have two angles and the included side of the one equal to two angles and the included side of the other, each to each, the triangles will be equal in all their parts. D In the triangles ABC and DEF, let the... | |
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VIf two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the... 
