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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. "
Elementary Geometry: With Applications in Mensuration - Page 112
by Charles Davies - 1850 - 216 pages
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 624 pages
...arcs AD, EG will be equal. For, if the radii CD, 0 G are drawn, the triangles ACD, E 0 G, having tlffe three sides of the one equal to the three sides of the other, each to each, are themselves equal (Prop. XVIII. Bk. I.) ; therefore the angle ACD is equal to the angle E 0 G (Prop....
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - 1863 - 448 pages
...each equal to CD, they will be equal to each other- Hence, the figure BAEF is a parallelogram (Bk- I- Th- xxv), and consequently, AE is equal to BF-...three sides of the one equal to the three sides of the olher, each to each, and therefore the angle ACE U equal to the angle BDF (Bk- I- Th- viii)THEOREM...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...the arcs AD, EG will be equal. For, if the radii CD, 0 G are drawn, the triangles ACD, E 0 G, having the three sides of the one equal to the three sides of the other, each to each, are themselves equal (Prop. XVIII. Bk. I.) ; therefore the angle ACD is equal to the angle E 0 G (Prop....
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1864 - 372 pages
...each equal to CD, they will be equal to each other- Hence, the figure BAEF is a parallelogram (Bk- I- Th- xxv), and consequently, AE is equal to BF/-...have the three sides of the one equal to the three tides of the other, each to each, and therefore the angle A CE IB equal to the angle BDF (Bk- I- Th-...
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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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Elements of Geometry and Trigonometry

C. Davies - 1867 - 342 pages
...each equal to CD, they will be equal to each other- Hence, the figure BAEF is a parallelogram (Bk- I- Th- xxv), and consequently, AE is equal to BF-...have the three sides of the one equal to the three bides of the other, each to each, and therefore the angle ACE IB equal to the angle BDF (Bk- I- Th-...
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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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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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