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" Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other. "
Plane Geometry, with Problems and Application - Page 34
by Herbert Ellsworth Slaught - 1918 - 332 pages
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Elements of Geometry with Exercises for Students: An an Introduction to ...

Aaron Schuyler - Geometry - 1876 - 384 pages
...BAC. For, BDC > BEG, EEC > BAC (53, 2). Hence, BDC > BAC (23, 20). 55. Proposition XVIII. — Theorem. Two triangles are equal if two sides and the included angle of tlie one are respectively equal to two sides and tlie included angle of the otlier. Let ABC and DEF...
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A Geometry for Beginners

George Anthony Hill - Geometry - 1880 - 332 pages
...with the same given parts, and prove that it is equal to the first. Theorem. — Two parallelograms are equal if two sides and the included angle of one...equal respectively to two sides and the included angle of the other. Exercises. — 1. Construct a parallelogram, the two sides being 44cm and 66cm, and the...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...672. Two triangles on the same sphere or on two equal spheres are either equal or symmetrical when two sides and the included angle of one are equal respectively to two sides and the included angle of the other. I. In the triangles ABC and DEF, let the sides AB and AC and the included angle A be...
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Lessons in Geometry: For the Use of Beginners

George Anthony Hill - Geometry - 1888 - 202 pages
...determined if one part is given ? If two parts are given? If the three angles are given? 14. Theorem. — Two triangles are equal, if two sides and the included...respectively, to two sides and the included angle of the other. HYPOTHESIS. A ABC and DEF, AB=DE, AC=DF, CONCLUSION. -^ BDE A ABC = A DEF. FI°- 67PROOF....
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Lessons in Geometry: For the Use of Beginners

George Anthony Hill - Geometry - 1888 - 200 pages
...determined if one part is given? If two parts are given ? If the three angles are given ? 14. Theorem. — Two triangles are equal, if two sides and the included...respectively, to two sides and the included angle of the other, HYPOTHESIS. A ABC and DEF, AB=DE, AC=DF, CONCLUSION. _ BDE A ABC = A DEF. ***- 67> PROOF....
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 264 pages
...PROPOSITION XXVI. THEOREM. 150. Two triangles are equal if two sides and the included angle of the one are equal respectively to two sides and the included angle of the other. A ~ BDE In the triangles ABC and DEF, let AB = DE, AC = DF, To prove A ABC=A DEF. Proof. Apply the A...
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Lessons in Geometry: For the Use of Beginners

George Anthony Hill - Geometry - 1889 - 200 pages
...determined if one part is given? If two parts are given? If the three angles are given? 14. Theorem. — Two triangles are equal, if two sides \ and the included angle of one are equal, respectively, vto two sides and the included angle of the other, HYPOTHESIS. j} A ABC and DEF, AB=DE, AC=DF, CONCLUSION....
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Pacific Educational Journal

Education - 1893 - 640 pages
...other. 12. Construct triangle by measuring two sides and included angle of a given triangle. Theorem: Two triangles are equal if two sides and the included...respectively, to two sides and the included angle of the other. 13. Theorem: i. In an isosceles triangle, the angles opposite the equal sides are equal....
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...which is not in the right bisector of a straight line is unequally distant from the ends of the line. and the included angle of one are equal respectively to two sides and the included angle of the other. 146. Theorem. Two triangles are equal if two angles and a side of one are equal respectively...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...prove AB > BC — A C. We have AB + AC > BC. PROPOSITION XV. THEOREM. 63. Two triangles are equal when two sides and the included angle of one are equal respectively to tivo sides and the included angle of the other. a ABDE In the triangles ABC and DEF, let AB = DE, AC...
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