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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 and Trigonometry - Page 19
by Adrien Marie Legendre - 1838 - 269 pages
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Marks' First Lessons in Geometry: Objectively Presented

Bernhard Marks - Geometry - 1869 - 180 pages
...angle c, opposite the side A B. I) B 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, Plane and Spherical: With Numerous Practical Problems

Horatio Nelson Robinson - 1869 - 276 pages
...remain ED = CF, (Ax. 3); but BE = AC, and AF= BD, (Th. 24); hence we have two A's, CAF and EBD, which have the three sides of the one equal to the three sides of the other, each to each; therefore, the two A's are equal, (Th. 21). If, from the whole figure ABDC, we take away the A CAF,...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1870 - 394 pages
...called a direct, and the latter an indirect demonstration. THEOREM via. If two triangles have tlie three sides of the one equal to the three sides of the other, each to each, the three angles will aho be equal, each to each. Let the two triangles ABC, ABD, have the side AB equal to the side AB,...
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Elements of geometry, containing the first two (third and fourth ..., Part 1

Euclides - 1871 - 136 pages
...If two angles of a triangle be.equal, the sides wMch tubtend them are also equal. (Eucl. i. 6.) SE 2 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. -25 q _ Let the three sides of the A s ABO, DEF be equal,...
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Marks' First Lessons in Geometry: In Two Parts : Objectively Presented and ...

Bernard Marks - Geometry - 1871 - 172 pages
...the side A B. THEOREMS ILLUSTRATED. 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 part's. Let the two triangles ABC, ADC, have the side AB of the one equal...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1871 - 302 pages
...the angle BAC must be greater than the angle EDF. Therefore, if two triangles, &c. PROPOSITION XV. THEOREM. If two triangles have the three sides of the one equal to trie '.hree sides of the other, each to each, the three angles will also be eqi. il, each to each,...
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...likewise those terminating in the other extremity of the base equal to one another. PROPOSITION VIII. If two triangles have the three sides of the one equal to the three sides of the other, each to each, then the triangles will also be equal to each other in every other respect, that is, the angles of...
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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 - 562 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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