 | Bernhard Marks - Geometry - 1869 - 172 pages
...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... | |
 | Euclides - 1871 - 136 pages
...sides wMch tubtend them are also equal. (Eucl. i. 6.) SE 2 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. -25 q _ Let the three sides of the A s ABO, DEF be equal,... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...mutually equilateral, they arc equivalent. Let ABC, DEF be two triangles which have the three sides of the one, equal to the three sides of the other, each to each, viz., AB to DE, AC to DF, and BC to EF ; then will the triangle ABC be equivalent to the triangle DEF.... | |
 | Bernard Marks - Geometry - 1871 - 172 pages
...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 part's. Let the two triangles ABC, ADC, have the side AB of the one equal... | |
 | Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...opposite to them are also equal. (Prop. V.) Let ABO and DEF be the two As having the three sides of the one equal to the three sides of the other, each to each. Let the ADEF be applied to the AABC so that the point D may coincide with the point A, and the line... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...EQUALITY OF TRIANGLES. PROPOSITION IX. 292. Theorem. — Two triangles which have the three sides of the one equal to the three sides of the other, each to each, are equal. DEM. — Let ABC and DEF be two triangles, in which AB = DE, AC = DF, and BC = EF ; then... | |
 | Edward Olney - 1872 - 270 pages
...that ABC may or may PROPOSITION IX. 292. Tlieorem.—Two triangles which have the three sides of the one equal to the three sides of the other, each to each, are equal DEM.—Let ABC and DEF be two triangles, in which AB = DE, AC = DF, and BC = EF; then are... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...angle A must be greater than the angle D. THEOREM XHI. 58. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles themselves will be equal. Let the triangles ABC, DEF have the side AB equal to DE, AC... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...EAG must be greater than 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 will be equal in all their parts. In the triangles ABC and 'DEF, let AB be equal to DE,... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...(26, Ax. 12). Thus circles having equal radii are equal ; and triangles having the three sides of the one equal to the three sides of the other, each to each, are also equal. Equal figures are always similar; but similar figures may be very unequal. 175. In... | |
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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. 
