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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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A Treatise on Special, Or Elementary Geometry

Edward Olney - Geometry - 1872 - 472 pages
...attention. A BD rV H E 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...
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A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872 - 566 pages
...receive special attention. EQUALITY OP TBIANGLES. 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...
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New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1873 - 202 pages
...coincide throughout (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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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 512 pages
...would be contrary to the hypothesis : hence, 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, AC...
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The elements of geometry, in eight books; or, First step in applied logic

L J V. Gerard - 1874
...perpendicular sides of the other, each to each, they are equal to each other. THEOREM 18. (Eucl. I. 8.) If two triangles have the three sides of the one equal to the three sides of the other, eaeh to each, they are equal to each other. Let ABC and DEF be two triangles having the sides AB, BC...
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New Elementary Geometry: With Practical Applications : a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1874 - 206 pages
...the arcs AD, EG will be equal. For, if the radii CD, OG are drawn, the triangles AC D, EOG, having the three sides of the one equal to the three sides of the other, each to each, are themselves equal (Theo. XIII. Bk. I. ) ; therefore the angle ACD is equal to the angle EOG (Theo....
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A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ...

Euclides - 1874
...so that the angles ARO and AOR are equal. Bisect RO in I) and join AD. Then the triangles ARD, AOD have the three sides of the one equal to the three sides of the other, and therefore by I. 8 we can prove the angles at A equal to one another and likewise the angles at...
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874 - 234 pages
...to the side DC, aud the side AD to the side BC. Join AC. Comparing the two triangles ABC and ADC, we have the three sides of the one equal to the three sides of the other (hyp. and const.). Therefore the alternate angles BAC and DCA are equal, (I. 6). and therefore AB is...
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First Lessons in Geometry: In Two Parts

B. Marks - 1875 - 176 pages
...angle c, opposite the side A B. DB 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...
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Elements of Geometry Containing Books I. to VI. and Portions of Books XI ...

James Hamblin Smith - Geometry - 1876 - 376 pages
...triangle be equal, the sides which subtend them are also equal. (Eucl. I. 6.) SB * PROPOSITION 0. THEOREM. 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. JS~ OS Let the three sides of the A s ABC, DEF be equal, each...
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