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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: With Practical Applications to Mensuration - Page 59
by Benjamin Greenleaf - 1863 - 320 pages
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1871 - 302 pages
...eqi. il, each to each, and the triangles themselves will be • •qua', Let ABC, DEF 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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A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872 - 566 pages
...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 are...
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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 are...
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter MASON - Geometry - 1872
...equal to each other, the ús 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...
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New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1873 - 202 pages
...to it ; hence the 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...
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New Elementary Geometry: With Practical Applications : a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1874 - 206 pages
...to it ; hence the angle A must be greater than the angle D. THEOREM XIII. 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,...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 512 pages
...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,...
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874 - 234 pages
...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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A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ...

Euclides - 1874
...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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The elements of geometry, in eight books; or, First step in applied logic

L J V. Gerard - 1874
...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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