 | Elias Loomis - Conic sections - 1849 - 252 pages
...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.... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...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 - 238 pages
...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,... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...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... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...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... | |
 | Charles Davies - Geometry - 1886 - 340 pages
...will be equal to tho angle K. For, draw the chord DE. Then the two triangles IKL and EAD, having the three sides of the one equal to the three sides of the other, each to each, the angle EAD will be equal to the angle K (Bk. I. Th. viii). PROBLEM 1X. Through a g1ven po1nt to... | |
 | 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,... | |
 | Thomas Lund - Geometry - 1854 - 520 pages
...coincide, and are equal, in all respects, as stated above. COR. Hence, also, if two triangles have the three sides of the one equal to the three sides of the other, each to each, in the same order, the two triangles will be equal, and their angles likewise will be equal, each to... | |
 | Charles Davies, William Guy Peck - Electronic book - 1855 - 592 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 bo equal." Prop.... | |
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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. 
