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 7by Adrien Marie Legendre - 1819 - 208 pagesFull view - About this book
| 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 - 418 pages
...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... | |
| Mathematical association - 1883 - 86 pages
...base being greater than the angle of the other. [By Rule of Conversion.] THEOR. 18. 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... | |
| Edward Olney - Geometry - 1883 - 352 pages
...triangles coincide, and are consequently equal. QED PROPOSITION VII. 305. Theorem.— Two triangles which have the three sides of the one equal to the three sides of the other, each to each, are equal. DEMONSTRATION. Let ABC and DEF be two triangles, in which AB = DE, AC = DF, and BO = EF.... | |
| Education - 1890 - 384 pages
...(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... | |
| Euclides, James Hamblin Smith - 1883 - 376 pages
...sides which subttnd them are also equal. (Kucl. I. 6.) SE PROPOSITION C. THEOREM. If two triangles ham the three sides of the one equal to the three sides of the otlwr, each to each, the triangles must be equal in all respects. Let the three sides of the A s ABC,... | |
| Mathematical association - 1884 - 146 pages
...is drawn to D the middle point of BC, shew that the angle ADB is acute. THEOK. 18. 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 angrles those are equal which are opposite to... | |
| F. B. Stevens - Examinations - 1884 - 202 pages
...to the product of its altitude and half the sum of its parallel sides. (LOOMIS.) 1. 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. 2. Two... | |
| Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...is drawn to D the middle point of BC, shew that the angle ADB is acute. THEOR. 18. 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... | |
| Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...than EF, then is the angle BAC greater than the angle EDF. PROPOSITION X. THEOREM. 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 in all respects. In the triangles ABC and DEF, let AB be equal to DE, AC to... | |
| |