| 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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