 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.  A School Geometry - Page xby Henry Sinclair Hall - 1908Full view - About this book
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...unequal,; the base of that which has the greater angle being greater than the base of the other. THEOR. 15. If two triangles have the three sides of the one equal to the three sides of the other, each to each, then the triangles are identically equal, and of the angles [Alternative proofs, (i) by Theors. 14... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...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 - 1877 - 58 pages
...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... | |
 | James Maurice Wilson - 1878 - 450 pages
...and HF together are greater than EF; (Th. 12.) therefore EG or BC is greater than EF. QED THEOREM 15. If two triangles have the three sides of the one equal to the three sides of the other, each to each, then the triangles are identically equal, and of the angles those are equal which are opposite to equal... | |
 | Euclides - 1878 - 398 pages
...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 pages
...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... | |
 | Universities and colleges - 1879 - 88 pages
...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 - Geometry - 1880 - 178 pages
...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 to 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... | |
 | Elias Loomis - Conic sections - 1880 - 452 pages
...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 - Geometry - 1881 - 418 pages
...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... | |
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