| Thomas J. Foster - Coal mines and mining - 1891 - 415 pages
...opposite or vertical angles are equal. 4. If two angles have their sides parallel they are equal. 5. If **two triangles have two sides and the included angle...the one, equal to two sides and the included angle** of the other, they are equal in all their parts. If two triangles have two angles and the included... | |
| Seth Thayer Stewart - Geometry - 1891 - 406 pages
...equal to the given lines, and it is, therefore, the required triangle. PROPOSITION I. 122. Theorem : // **two triangles have two sides and the included angle of the one equal to two sides and the included** anyle of the other, each to each, they are equal in all their parts. Statement : Let the two triangles... | |
| Henry Smith Carhart, Horatio Nelson Chute - Physics - 1892 - 382 pages
...triangles .4KB and A'KB, we have the angles at A' equal, and hence right angles, and AK= A'K, since the **triangles have two sides, and the included angle of the one equal to** the corresponding parts of the other. dicular to MN, and A' is as far back of MN as A is in front.... | |
| Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 395 pages
...C. PROPOSITION XLII. THKOREM. 127. Two parallelograms which have two tides and the included angle of **one equal to two sides and the included angle of the other, each to each,** are equal in aU respect*. I) Let AD and A' D' represent, two parallelograms in whicli AB equal* A'... | |
| Ephraim Hunt - Geometry - 1894 - 99 pages
...ABC and DEF are equal in all respects. Because, (1) We have made two sides and the included angle of **one equal to two sides and the included angle of the other, each to each.** (2) Put the vertex D upon vertex A; side DE upon side AB, and as they are equal, the point E will fall... | |
| Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 320 pages
...are called reciprocal. The relation is more clearly seen by resorting to parallel columns. Th. 1. If **two triangles have two sides and the included angle of the one** respectively equal to two sides and the included angle of the other, the triangles are congruent. Th.... | |
| Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 320 pages
...reciprocal. The relation is more clearly seen by resorting to parallel columns. 22 TRIANGLES. Th. 1. If **two triangles have two sides and the included angle of the one** respectively equal to two sides and the included angle of the other, the triangles are congruent. Th.... | |
| Henry Dallas Thompson - Geometry, Solid - 1896 - 199 pages
...triangle be supplementary, the vertex of the triangle lies on a fixed great circle. 26. If two spherical **triangles have two sides and the included angle of the one equal** respectively to two sides and the included angle of the other, the two triangles are equal or symmetrical.... | |
| Henry W. Keigwin - Geometry - 1897 - 227 pages
...greater quantity last. a > 6 ) a> b'\ TRIANGLES. INTERSECTING LINES. PROPOSITION I. THEOREM. 44. If **two triangles have two sides and the included angle of the one equal** respectively to two sides and the included angle of the other, the two triangles are equal. X / " \... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 354 pages
.... Hyp. AX=AX, Iden. angle C4^T= angle C'AX. Cons. Hence triangle /4 CX— triangle A C'X. §78 [If **two triangles have two sides, and the included angle of the one equal** respectively to two sides and the included angle of the other, the triangles are equal.] Hence XC=XC.... | |
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