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" 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 Text-book of Geometry - Page 39
by George Albert Wentworth - 1893 - 437 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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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...Z BCH=ZA + Z B. PROI-OSITION XXIII. THEOREM. 106. Two triangles are equal in all respects when two sides and the included angle of the one are equal respectively to two sides and the included angle of the other. D Ai In the triangles ABC and A' B' C', let AB = A' B', AC = A' C', ZA = Z A'. We are...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 426 pages
...PROPOSITION XXIII. THEOREM. 106. Two triangles are equal in all respects when two sides and the iucluded angle of the one are equal respectively to two sides and the included angle of the other. C' B A' In the triangles ABC and A' B' C', let AB = A'B', AC= A' C',Z. A=Z. A'. We are...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...С Б, AС=BС, СE=С E, Hyp. Iden. Cons. §106 (two A are equal when two sides and the included Z of the one are equal respectively to two sides and the included ¿ of the other). (being homologous A of equal &, ). a. E. o. PROPOSITION XXIX. THEOREM. 113. A straight...
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Elementary Geometry: Congruent Figures

Olaus Henrici - Congruences (Geometry) - 1879 - 218 pages
...(§ 172). This gives Theorem : Two triangles are congruent if two 'sides and the included angle in the one are equal respectively to two sides and the included angle in the other. § 1 88. A quadrilateral is, thirdly, a kite, if one diagonal bisects the angles at the...
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Elements of Geometry

George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...AC=BC, CE=CE, ZA CE = Z BСЕ; Hyp. Iden. Cons. §106 (two A are equal when two sides and the included Z of the one are equal respectively to two sides and the included Z of the other). (being homologous A of equal A ). QED Ex. If the equal sides of an isosceles triangle...
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Elements of Geometry

George Albert Wentworth - Geometry, Modern - 1882 - 268 pages
...GEOMETRY. BOOK I. PROPOSITION XXIII. THEOREM. 106. Two triangles are equal in all respects when two sides and the included angle of the one are equal respectively to two sides and the included angle of the other. В AI la the triangles ABC and A' B' C', let AB = A' B', We are to prove Д AB С = Д...
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Elements of Plane Geometry

Franklin Ibach - Geometry - 1882 - 208 pages
...diagonal of a parallelogram divides it into two equal triangles. THEOREM XLI. 131. Tivo parallelograms are equal if two sides and the included angle of the one are respectively equal to two sides and the included angle of the other. Let ABCD and EFGH be two os, having...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1886 - 394 pages
...angles of the one THEOREM VI. 124. Two triangles are congruent if two sides and the included angle in the one are equal respectively to two sides and the included angle in the other. « r B HYPOTHESIS. ABC and LMN two triangles, with AB = LM, BC = MN, VB = £ Af. CONCLUSION....
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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 angle of one are equal, respectively, to two sides and the included angle of the other. HYPOTHESIS. A ABC and...
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