 | American fiction - 1895 - 540 pages
...verse of poetry. Let us now consider another form of the proof. 282 The Sewanec Review. of the one equal to the three sides of the other, each to each, therefore they are equal ; hence, the angle BCA, opposite the side AB, is equal to the angle CAE, opposite to... | |
 | William James Milne - Geometry - 1899 - 404 pages
...what conditions are two triangles equal ? /^Theorem. Two triangles are equal, if the three sides of one are equal to the three sides of the other, each to each. E Data : Any two triangles, as ABC and DEF, in which AB = I>E, AC = DF, and BC = EF. To prove triangles... | |
 | William James Milne - Geometry, Modern - 1899 - 258 pages
...Under what conditions are two triangles equal ? Theorem. Two triangles are equal, if the three sides of one are equal to the three sides of the other, each to each. D Data: Any two triangles, as ABC and DEF, in which AB = J>E, AC = DF, and BC = EF. To prove triangles... | |
 | Euclid, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...another. Hence we are led to the following important Corollary. COROLLARY. If in two triangles fhe three sides of the one are equal to the three sides of the other, each to each, then the triangles are equal in all respects. [An alternative proof, which is independent of Prop.... | |
 | Euclid - Euclid's Elements - 1904 - 488 pages
...one another. Hence we are led to the following important Corollary. COROLLARY. If in two triangles the three sides of the one are equal to the three sides of the other, each to each, then the triangles are equal in all respects. [An alternative proof, which is independent of Prop.... | |
 | David Allan Low - Geometrical drawing - 1912 - 468 pages
...respect. The different cases are as follows : — Two triangles are equal in every respect when — (1) The three sides of the one are equal to the three sides of the other, each to each. (2) Two sides and the included angle in one are equal to two sides and the included angle in the other,... | |
 | Mathematics - 1917 - 284 pages
...(Construction) /. A SIF = A SFC (76) /. ZI = ZC (72c) QED 78a. Theorem: Two triangles are equal if the three sides of the one are equal to the three sides of the other. Given: In the A ABC and DEF, let DE = AB, DF = AC, and EF = BC. To Prove: A DEF = A ABC. Proof: Place... | |
 | Surveying - 1888 - 388 pages
...equal, as also for the same reason BM is equal to BI ; hence the two triangles AMB, AIB are equal, as the three sides of the one are equal to the three sides of the other, and the angle AMB is equal to AIB, and consequently equal to the angle amb. The second property is... | |
 | Mathematics - 1867 - 426 pages
...sides of the other, each to each, is based upon the particular case that two triangles are equal when the three sides of the one are equal to the three sides of the other, not only each to each, but each to either ; that is, when the two triangles are equilateral and the... | |
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THEOREM. 43. 7\»o triangles are equal, when the three sides of the one are equal to the three sides of the other, each to each. 
