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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 will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal...
Elementary Geometry: With Applications in Mensuration - Page 97
by Charles Davies - 1850 - 216 pages
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## Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 288 pages
...angles. THEOREM. 36. Two triangles are equal, when two sides and the included angle of the one are equal to two sides and the included angle of the other, each to each. Demonstration. In the two triangles ABC, DEF (fig. 23), Fig. 23 let the angle A be equal to the angle...
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## Psychology: Or, Elements of a New System of Mental Philosophy, on the Basis ...

Samuel Simon Schmucker - Psychology - 1842 - 262 pages
...demonstration of the theorem of Euclid known as Prop. IV. of Book I., viz. : If two triangles have two sides, and the included angle of 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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## Arithmetical Spyglass and Teacher's Assistant: Intended as a Key and ...

Charles Waterhouse - Arithmetic - 1842 - 178 pages
...Demonstrably true: — 1. Two triangles are equal when two sides and the included angle of the one are equal to two sides and the included angle of the other, each to each. 2. In an isosceles triangle, the angles opposite to the equal sides are equal. 3. Of the two sides...
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## Elementary and practical Arithmetic on the inductive system, by analysis and ...

Charles WATERHOUSE - Arithmetic - 1844 - 228 pages
...opposite the longer aids. 6. Two triangles ore equal when two sides and the included angle of the one are equal to two sides and the included angle of the other, each to each. 7. Every triangle is half of a parallelogram of the same base and altitude. 8. In a right-angled triangle,...
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## Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 326 pages
...parallel, the angle BAC is equal to its alternate angle DCA (Prop. xvii)t; hence the two triangles, having two sides and the included angle of the one equal to two sides and the included angle of the other, namely, the side AB equal to. the side CD, the side AC common, and the contained angle...
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## Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 372 pages
...by the successive angles ACB, BCD, DCE, ECF. FCA. PROPOSITION V. THEOREM. 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 tc each, the two triangles will be equal Let the side ED be equal to the side BA, the side DF to the...
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## Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...CD, and BC is common to the two triangles ABC, BCD, the two triangles ABC, BCD have two sides and C the included angle of the one, equal to two sides and the included angle of the other; therefore, the side AC is equal to BD (Prop. VI.), and the angle ACB to the angle CBD....
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## The Logic and Utility of Mathematics: With the Best Methods of Instruction ...

Charles Davies - Logic - 1850 - 390 pages
...each, and the triangles themselves will be equal." Prop. V. " When two triangles have two Proposition sides and the included angle of the one, equal to...and the included angle of the other, each to each, the two triangles will be equal." Axiom I. " Things which are equal to the Axioms, same thing, are...
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## The Logic and Utility of Mathematics: With the Best Methods of Instruction ...

Charles Davies - Logic - 1850 - 402 pages
...to each, and the triangles themselves will be equal." Prop. V. " When two triangles have two tides and the included angle of the one, equal to two sides...and the included angle of the other, each to each, the two triangles will be equal." Axiom I. " Things which are equal to the same thing, are equal to...
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## Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...BAC is equal to its alternate angle DCA, (Prop, xvu;) hence the two triangles, having two sides^and the included angle of the one equal to two sides and the included angle of the other, namely, the side equal to the side CD, the side AC common, and the contained angle BAC...
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