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. Elements of Geometry - Page 9by Adrien Marie Legendre - 1825 - 224 pagesFull view - About this book
| Euclides - 1874 - 120 pages
...so that the angles ARO and AOR are equal. Bisect RO in I) and join AD. Then the triangles ARD, AOD have the three sides of the one equal to the three sides of the other, and therefore by I. 8 we can prove the angles at A equal to one another and likewise the angles at... | |
| B. Marks - 1875 - 176 pages
...opposite the 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... | |
| Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...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, James Hamblin Smith - Geometry - 1876 - 376 pages
...sides 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,... | |
| Euclides - 1877 - 58 pages
...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
...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, James Hamblin Smith - Geometry - 1878 - 398 pages
...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 - 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
...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... | |
| Charles Scott Venable - 1881 - 380 pages
...XIII. 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) the angle... | |
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