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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 - Page 9
by Adrien Marie Legendre - 1825 - 224 pages
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1866 - 328 pages
...the angle A must be greater than the angle D. PROPOSITION XVIII. — THEOREM. 80. 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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Outlines of Mathematical Science for the School Room

Charles Davies - Mathematics - 1867 - 186 pages
...need the following, which have been before proved ; viz. : Prop. X. (of Legendre). "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." Prop. V. " If two triangles have two sides and the...
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Elements of Geometry and Trigonometry

C. Davies - 1867 - 342 pages
...EAD will be equal to the angle KFor, draw the chord DE- Then the two triangles IKL and EAD, having the three sides of the one equal to the three sides of the other, each to each, the angle EAD will be equal -o the angle K (Bk- I- Th- viii)PROBLEM IXThrough a g1ven point to draw...
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The New York Teacher, and the American Educational Monthly, Volume 5

Education - 1868 - 516 pages
...the other. " — Campbells Rhet. This structure is very often neglected. Examples : "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." The article before one here is improper, because the...
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Elementary Geometry, Volume 1

James Maurice Wilson - Geometry - 1868 - 132 pages
...be constructed so as to have its sides equal to three given lines, it is clear that if two triangles have the three sides of the one equal to the three sides of the other, these triangles must be identical, or be equal in all respects. And a similar remark may be made on...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1868 - 340 pages
...than ABC. PROPOSITION XVII. — THEOREM. ELEMENTS OP GEOMETRY. Let ABC, DBF be two triangles, having the three sides of the one equal to the three sides of the other, eaeh to each, namely, AB to DE, AC toDF, andCB toEF; then their triangles will be equivalent. Let 0...
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Elements of Geometry, Plane and Spherical: With Numerous Practical Problems

Horatio Nelson Robinson - 1869 - 276 pages
...the theorem; the difference between any two sidei of a triangle, etc. THEOREM XXI. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the two triangles are equTl, and the equal angles are opposite the equal sides. In two triangles, as...
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Marks' First Lessons in Geometry: Objectively Presented

Bernhard Marks - Geometry - 1869 - 172 pages
...THEOREMS ILLUSTRATED. 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 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...
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Elements of geometry, containing the first two (third and fourth ..., Part 1

Euclides - 1871 - 136 pages
...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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