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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. "
Elements of Geometry, Conic Sections, and Plane Trigonometry - Page 27
by Elias Loomis - 1877 - 443 pages
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Elements of Plane Geometry: For the Use of Schools

Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...are equal (Def. 4), therefore AD=DB (BI Prop. 19, Cor. 2); hence the two triangles ACD, BCD, having the three sides of the one equal to the three sides of the other, are equal, (B. I. Prop. 22), and the angles ACD, BCD, are equal ; and therefore the arcs AE, EB,are...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 130 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,...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 130 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,...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 pages
...AP, since PB = PC, the oblique line AB = AC (B. VI, Prop, v) ; therefore the two triangles ADB, ADC have the three sides of the one equal to the three sides of the other ; consequently they are equal (BI, Prop, vm), and the angle ADB is equal to ADC ; therefore each is...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...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...
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The Logic and Utility of Mathematics,: With the Best Methods of Instruction ...

Charles Davies - Logic - 1850 - 375 pages
...proposition, we need the following, which have been before proved ; viz. : Prop. X. (of Legendre). "When two triangles have the three sides of the one equal...each, and the triangles themselves will be equal." Prop. V. " When two triangles have two Propositio„ sides and the included angle of the one, equal...
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The Logic and Utility of Mathematics: With the Best Methods of Instruction ...

Charles Davies - Logic - 1850 - 390 pages
...Legendre). "When two triangles Previous have the three sides of the one equal to the three tmths^eces" sides of the other, each to each, the .three angles...each, and the triangles themselves will be equal." Prop. V. " When two triangles have two Proposition sides and the included angle of the one, equal to...
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The Logic and Utility of Mathematics: With the Best Methods of Instruction ...

Charles Davies - Logic - 1850 - 375 pages
...Legendre). " When two triangles p^.,,^ have the three sides of the one equal to the three lnah " """"' tides of the other, each to each, the three angles will...each, and the triangles themselves will be equal." Prop. V. " When two triangles have two tides and the included angle of the one, equal to two sides...
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...AP, since PB = PC, the oblique line AB = AC, (B. VI, Prop. v;) therefore the two triangles ADB, ADC have the three sides of the one equal to the three sides of the other; consequently they are equal, (B. I, Prop, viu,) and the angle ADB is equal to ADC ; therefore each...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 218 pages
...chord, 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...
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