 | 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,... | |
 | 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)... | |
 | 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... | |
 | Euclides - 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... | |
 | 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... | |
 | 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... | |
 | 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,... | |
 | 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,... | |
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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. 
