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" If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects. "
Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ... - Page 416
by Robert Mudie - 1836 - 496 pages
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...respects. (a) Anyone of the angles of a triangle is less than two right angles cor. 5 (A) Triangles which have two sides and the included angle of the one equal to two sides, and the included angle of the other, each to each, are equal in all respects . . .5 (c) Triangles which have two angles and...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...respeits. (aj Any one of the angles of a triangle is less than two right angles cor. 5 (б) Triangles which have two sides and the included angle of the one equal to two sides, and the included angle of the other, each to each, are equal in all respects . . .5 (r) Triangles which have two angles and...
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Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

Robert Mudie - Mathematics - 1836 - 542 pages
...between them, arc given, there are sufficient data for constructing the triangle ; 416 CONSTRUCTION OF TRIANGLE?. and if two triangles have two sides and...that it is not the sum of the sides which is equal, but that each of the two sides of the one triangle, taken singly, is equal to one side of the other...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 394 pages
...the four right angles, as by the successive angles ACB, BCD, DCE, ECF, FCA. PROPOSITION V. THEOREM. ' If two triangles have two sides and the included angle...the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal. Let the side ED be equal to the side BA,...
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Elements of Geometry, Theoretical and Practical: Including Constructions of ...

Eugenius Nulty - Geometry - 1836 - 242 pages
...conditions which determine such equality are comprised in the four following theorems. THEOREM VI. 38. If two triangles have two sides, and the included angle of the one respectively equal to two sides and the included angle of the other, the remaining sides and angles...
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First Lessons in Geometry: With Practical Applications in Mensuration, and ...

Charles Davies - Geometrical drawing - 1840 - 264 pages
...of the Triangle. SECTION VI. PROPERTIES OF THE TRIANGLE. 1. If two triangles have two sides, and an included angle of the one, equal to two sides and the included angle of the other, each to each, the remaining parts will also be equal. That is, if we have the two triangles,...
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Psychology: Or, Elements of a New System of Mental Philosophy, on the Basis ...

Samuel Simon Schmucker - Psychology - 1842 - 262 pages
...the nature, eg, of the demonstration of the theorem of Euclid known as Prop. IV. of Book I., viz. : If two triangles have two sides, and the included...the one equal to two sides and the included angle of the other, they must be identical or equal in all respects. For it virtually consists in supposing...
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Elementary Course of Geometry ...

Charles William Hackley - Geometry - 1847 - 248 pages
...to the second. PROP. IX. Two spherical triangles are either identical or symmetrical, 1°. When they have two sides and the included angle of the one equal to the same in the other ; 2°. When they have a side and two adjacent angles ; 3°. When they have three...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 326 pages
...parts, by the line CD, making the angle ACD equal to the angle BCD. Then the two triangles ADC and BDC have two sides and the included angle of the one equal to the two sides and the included angle of the other, namely, the side AC equal to BC, the angle ACD equal...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...formed at the point of intersection, are together equal to four right angles. PROPOSITION VI. THEOREM. If two triangles have two sides, and the included...the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal, their third sides will be equal, and their...
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