 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...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. In ^s CBA, CDA,... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...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. In ^s CBA, CDA,... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...will intersect in two points G and H, thus giving two triangles DGF and DHF ; but these two triangles, having the three sides of the one equal to the three sides of the other, are identical (Prop. vm). If two of the given lines are equal, the triangle will be isosceles ; when... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...also be equal, each to each, and the triangles themselves will be equal. Let ABC, DBF be two triangles having the three sides of the one equal to the three sides of the other, viz.: AB equal to DE, BC to EF, and AC to DF ; then will the three angles also be equal, viz.: the... | |
 | Charles Davies - Logic - 1850 - 398 pages
...following, which have been before proved ; viz. : Prop. X. (of Legendre). "When 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." Prop. V.... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...will intersect in two points G and H, thus giving two triangles, DGF and DHF; but these two triangles, having the three sides of the one equal to the three sides of the other, are identical. (Prop, vin.) If two of the given lines are equal, the triangle will be isosceles; when... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...and the arc AE equal to EB. First. Draw the two radii CA, CB. Then the two triangles A CD, DCB, have the three sides of the one equal to the three sides of the *Note. When reference is made from one theorem to another, in the same Book, the number of the theorem... | |
 | Charles Davies - Geometry - 1850 - 238 pages
...and the arc AE equal to EB. First. Draw the two radii CA, CB. Then the two triangles A CD, DCS, have the three sides of the one equal to the three sides of the Of the Circle. B other, each to each : viz. AC equal to CB, being radii, AD equal to DB, by hypothesis,... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...the hypothesis : therefore, BA C is greater than EDF. PROPOSITION X. THEOEEM. 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. Let EDF and BAC be two triangles, having the side ED=BA, the side EF^BC, and the... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...hypothesis : therefore, BA C is greater than EDF. PROPOSITION X. THEOREM. If two triangles have ihe three sides of the one equal to the three sides of the other, each to each, the triangles are equal. Let EDF and BA C be two triangles, having the side ED=BA, the side EF=BC, and... | |
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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. 
