 | Seth Thayer Stewart - 1891 - 422 ページ
...PC, QD, QE, and QF are equal. The triangles PAC and Q 0 E are, then, isosceles triangles, and they have the three sides of the one equal to the three sides of the other, each to each. The same is true of the triangles PAB and QDF; and, also, of PBC and QF E. The corresponding isosceles... | |
 | Seth Thayer Stewart - 1891 - 428 ページ
...: / 2 3 and 456 being any two triangles, etc. PROPOSITION III. 134. Theorem : If two triangles have three sides of the one equal to the three sides of the other, each to each, they are equal in all their parts. AS Statement: Let the two triangles A CB and HFE have the side AC... | |
 | Seth Thayer Stewart - 1891 - 428 ページ
...: / 2 3 and 456 being any two triangles, etc. PROPOSITION III. 134. Theorem : If two triangles have three sides of the one equal to the three sides of the other, each to cucli, they are equal in all their parts. Statement: Let the two triangles AC B and H FE have the side... | |
 | Euclid - 1892 - 460 ページ
...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. The following proof of Prop. 8 is worthy of attention as it is independent of... | |
 | 1895 - 540 ページ
...he would a 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... | |
 | Paul Henry Hanus - 1893 - 76 ページ
...three wires, he sees that three lines determine only one triangle, and hence that all triangles having the three sides of the one equal to the three sides of the other each to each are equal. In early instruction then the presentation of a new subject, and of each new phase of a... | |
 | George Cunningham Edwards - 1895 - 330 ページ
...figure may be substituted for another and may be made to occupy exactly B Fro. 24. TRIANGLES. THEOREM. If two triangles have the three sides of the one equal to the three sides of the other, each to each, they are congruent. If the two triangles (p) and (g) having : AB=DE, BC = DF, and AC=EF, be so placed... | |
 | Elias Loomis - 1895 - 450 ページ
...Therefore, if two triangles, etc. PROPOSITION XV. THEOREM. If two triangles have the three sides oftJie one equal to the three sides of the other, each to each, the three angles will also bc equal, each to each, and the triangles themselves will be equal. Let... | |
 | 1896 - 564 ページ
...proof. Mr. Venable's proof of the same proposition is about as follows : The two triangles BAG, ACE, have the three sides 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... | |
 | Frank H. Hall - 1898 - 296 ページ
...angles of a triangle are equal, two of the sides are equal. 3. If two triangles have the three sides of one equal to the three sides of the other, each to each, do you think the two triangles are alike in every respect ? 4. If two triangles have the three angles... | |
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If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent. 
