 If two triangles have the three sides of the one respectively equal to the three sides of the other, the triangles are congruent, C Given A ABC, AB'C, with AB = AB', BC = B'C, and AC = AC.  New Plane and Solid Geometry - Page 40by Wooster Woodruff Beman, David Eugene Smith - 1899 - 382 pagesFull view - About this book
 | Charles Butler - 1814 - 582 pages
...biilh true, are not in all cases so ; one may be true, and the other false : thu», tin proposition, " If two triangles have the three sides of the one respectively equal to the three sides of the other, the three angles of the one will be respectively equal to the three augles of the other," may be proved... | |
 | George Lees - 1826 - 276 pages
...same manner, it may be proved, that AH is equal to DF ; hence the two triangles AGH, and DEF having the three sides of the one respectively equal to the three sides of the other are equal in every respecta ; and therefore, the angle at A equal to the angle at D, the angle AGH,... | |
 | John Radford Young - Euclid's Elements - 1827 - 246 pages
...the angle D, it must necessarily be greater. PROPOSITION XXV. THEOREM. Two triangles are equal which have the three sides of the one respectively equal to the three sides of the other. For the angle included between any two sides in the one triangle must be equal to the angle included... | |
 | Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...upon D, and B upon E, the line AB would coincide with DE ; hence the two triangles ACB, DCE, having the three sides of the one respectively equal to the three sides of the other, are equal (BI Prop. 22), and the angles ACB, DCE,are equal. Cor. 1. Equal chords subtend equal angles... | |
 | Scottish school-book assoc - 1845 - 444 pages
...equiangular triangle is also equilateral. PROPOSITION IX. — THEOREM. If two triangles, ABC and DEF. have the three sides of the one respectively equal to the three sides of the other, the triangles shall be equal in all respects, and have those angles equal, that are opposite to equal sides. Let... | |
 | Nathan Scholfield - 1845 - 894 pages
...hypothesis ; therefore, BAG is greater than EDF. PROPOSITION XIII. THEOREM. Two triangles are equal, which have the three sides of the one, respectively equal to the three sides of the other. Let the side ED=BA, the side EF=BC, and the side DF=AC ; then will the angle D=A, the angle E=B. and... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...&c. COR. — Hence every equiangular triangle is equilateral. PROP. VII. THEOR. If two triangles have three sides of the one respectively equal to the three sides of the other, each to each, the triangles are equal, and the angles are equal which are opposite to the equal sides.... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...&c. COR.—Hence every equiangular triangle is equilateral. PROP. VII. THEOR. If two triangles have three sides of the one re-spectively equal to the three sides of the other, each to each, the triangles are equal, and the angles are equal which are opposite to the equal sides.... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...between the sides CB and CA, and therefore the triangle is isosceles. 'IPROPOSITION VIII. .THEOREM. When two triangles have the three sides of the one respectively equal to tlie three sides of the other, the triangles will be identical, and equal in all respects. Let the... | |
 | Euclides - Geometry - 1853 - 334 pages
...extremity B equal, which do not coincide with one another. Which was to be proved. PEOP. VIII. THEOE. If two triangles have the three sides of the one respectively equal to the three sides of the other : then these triangles shall be equal in every respect, ie (1) the three angles of the one shall he... | |
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