 | Euclides - 1877 - 58 ページ
...with AB, shew that AC and BD are also equal and make equal angles with AB. PROPOSITION VIII. THEOREM. If two triangles have the three sides of the one equal to the three sides of the other, each to each ; the two triangles shall be equal in all respects. Let ABC, DEF be two triangles, in which AB is equal... | |
 | Elias Loomis - 1877 - 458 ページ
...BAC must be greater than the angle EDF. Therefore, if two triangles, etc. PROPOSITION XV. TIIEOREM. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the three angles will also be equal, each to each, and the triangles themselves will be equal. Let... | |
 | Euclides - 1878 - 398 ページ
...triangle be equal, the sides which subttnd them are also equal. (Bucl. I. 6.) SE PROPOSITION C. THEOREM. If two triangles have the three sides of the one equal to the three sides of the otlwr, each to each, the triangles must be equal in all respeett. Let the three sides of the A s ABC,... | |
 | Euclides, James Hamblin Smith - 1879 - 376 ページ
...by a process like that in Prop. A, we can prove the following theorem : PROPOSITION C. THEOREM. // two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles must be equal in all respects. Let the three sides of the A s ABC, DEF be equal, each... | |
 | 1879 - 88 ページ
...figure. What are similar figures? Name the classes of quadrilaterals. Prove that two triangles with the three sides of the one equal to the three sides of the other, each to each, are equal. Prove that the three angles of a triangle are equal to two right angles. Prove that the... | |
 | Euclides, Frederick Burn Harvey - 1880 - 178 ページ
...and therefore this case is to be dismissed. Wherefore, Upon the same base, QED PROP. VIII. THEOREM. If two triangles have the three sides of the one equal...the three sides of the other, each to each, then the angle which is contained by any two sides of the one triangle shall be equal to the angle contained... | |
 | Elias Loomis - 1880 - 452 ページ
...BAC must be greater than the angle EDF. Therefore, if two triangles, etc. PROPOSITION XV. THEOREM. If two triangles have the three sides of the one equal to the threo sides of the other, each to each, the three angles will also be equal. each to each, and the... | |
 | Simon Newcomb - 1881 - 418 ページ
...equal (1), 3. Comparing with the last two equations of (1), it is seen that the triangles BFD and AEC have the three sides of the one equal to the three sides of the other. Therefore Triangle A EC = triangle BFD. 4. From the trapezoid ABED take away the triangle A EC, and... | |
 | Mary W I. Shilleto - 1882 - 418 ページ
...students are advised not to confine themselves to one paper, but to make use of the whole set. (a) 1. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles must be equal in all respects. From every point of a given line, the lines drawn to each... | |
 | 1890 - 384 ページ
...physical ligure (as surface or solid) and a mathematical figure (as area or volume). 3. Prove that if two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are equal. 4. Jf the area of a triangle, whose shortest side is six feet, is 4 .4 square... | |
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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. 
