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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...: Translated from the French for the Use of the ... - Σελίδα 9
των Adrien Marie Legendre, John Farrar - 1825 - 224 σελίδες
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Outlines of Mathematical Science for the School Room

Charles Davies - 1867 - 186 σελίδες
...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...

Elements of Geometry and Trigonometry

C. Davies - 1867 - 342 σελίδες
...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...

The New York Teacher, and the American Educational Monthly, Τόμος 5

1868 - 516 σελίδες
...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...

Elementary Geometry, Τόμος 1

James Maurice Wilson - 1868 - 132 σελίδες
...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...

Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - 1868 - 340 σελίδες
...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...

Marks' First Lessons in Geometry: Objectively Presented

Bernhard Marks - 1869 - 172 σελίδες
...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...

Elements of Geometry, Plane and Spherical: With Numerous Practical Problems

Horatio Nelson Robinson - 1869 - 276 σελίδες
...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...

Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - 1870 - 394 σελίδες
...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...

Elements of geometry, containing the first two (third and fourth ..., Μέρος 1

Euclides - 1871 - 136 σελίδες
...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,...

Marks' First Lessons in Geometry: In Two Parts : Objectively Presented and ...

Bernard Marks - 1871 - 172 σελίδες
...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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