 | 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)... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
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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. 
