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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. "
Principles of Plane Geometry - Page 13
by James Wallace MacDonald - 1889 - 63 pages
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Elements of Geometry, Plane and Spherical: With Numerous Practical Problems

Horatio Nelson Robinson - 1869 - 276 pages
...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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Marks' First Lessons in Geometry: Objectively Presented

Bernhard Marks - Geometry - 1869 - 172 pages
...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 the first two (third and fourth ..., Part 1

Euclides - 1871 - 136 pages
...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, each to each,...
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Marks' First Lessons in Geometry: In Two Parts : Objectively Presented and ...

Bernard Marks - Geometry - 1871 - 172 pages
...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
...mutually equilateral, they arc equivalent. Let ABC, DEF be two triangles which have the three sides of the one, equal to the three sides of the other, each to each, viz., AB to DE, AC to DF, and BC to EF ; then will the triangle ABC be equivalent to the triangle DEF....
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A Treatise on Special Or Elementary Geometry

Edward Olney - 1872 - 270 pages
...that ABC may or may PROPOSITION IX. 292. Tlieorem.—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 - 216 pages
...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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A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1872 - 472 pages
...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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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...are also equal. (Eucl. i. 6.) PBOP. C. THEOREM. If two triangles have the three sides of the one eqwl to the three sides of the other, each to each, the triangles must be equal in all respects. Let the three sides of the A s ABC, DEF be equal, each to each, that...
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New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1873 - 202 pages
...(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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