| B. Marks - 1875 - 176 pages
...side A B. DB PROPOSITION XIX. THEOREM. DEMONSTRATION. We wish to prove that, If two triangles have **the three sides of the one equal to the three sides of the other, each to each,** they are equal in all their parts. Let the two triangles ABC, ADC, have the side AB of the one equal... | |
| James Hamblin Smith - Geometry - 1876 - 376 pages
...which subtend them are also equal. (Eucl. I. 6.) SB * PROPOSITION 0. THEOREM. 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. JS~ OS Let the three sides of the A s ABC, DEF be equal,... | |
| Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...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
...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
...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
...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,... | |
| 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 angle... | |
| Euclid, F. B. Harvey - Geometry - 1880 - 119 pages
...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... | |
| Charles Scott Venable - 1881 - 382 pages
...THEOREM. .the vertex A, and D, the middle point of the base, BC ; the two triangles ABD, ADC, have **the three sides of the one equal to the three sides of the other, each to each** ; namely, AD common, AB = AC by hypothesis, and BD = DC by construction ; therefore (by the last Proposition)... | |
| Simon Newcomb - Geometry - 1881 - 418 pages
...(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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