| 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... | |
| Euclides - 1877
...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 to... | |
| James Maurice Wilson - 1878
...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
...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
...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 to... | |
| Universities and colleges - 1879 - 86 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... | |
| Euclid, F. B. Harvey - Geometry - 1880 - 119 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... | |
| 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... | |
| Mary W I. Shilleto - 1882
...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... | |
| Marianne Nops - 1882
...proposition. SUMMARY OP PROPOSITION VIII., THEOREM 5. If in two triangles the, three sides of one are **equal to the three sides of the other each to each, the** triangles are equal in all respects. Cons.— Nil. AAA Proof. — By superposition. If the triangles... | |
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