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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. "
Elements of Plane Geometry - Page 48
by Thomas Hunter - 1878 - 132 pages
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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, .ABC and DEF, having...
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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 - 240 pages
...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 angle...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
...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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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 and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 384 pages
...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...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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