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 (sas = sas). Hyp. In A ABC and A'B'C', AB = A'B', BC = B'C', and Z B = Z B'. Plane Geometry - Page 14by Arthur Schultze - 1901Full view - About this book
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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.... | |
| George Albert Wentworth - Geometry - 1888 - 264 pages
...equal respectively to the hypotenuse and an acute angle of the other. PROPOSITION XXVI. THEOREM. 150. Two triangles are equal if two sides and the included...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.... | |
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