 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'.  Secondary-school Mathematics - Page 55by Robert Louis Short, William Harris Elson - 1910Full view - About this book
 | Arthur Schultze - 1901 - 260 pages
...divides the figure into two equal triangles. PROPOSITION III. THEOREM 72. 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'. To prove... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...CBD, is greater than either of the opposite interior angles, A or C. PROPOSITION XIX. — THEOREM. Two triangles are equal when two sides and the included angle of the one are respectively equal to two sides and the included angle of the other. Given. — Let ABC and DEF be... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...divides the figure into two equal triangles. PROPOSITION III. THEOREM 72. Two triangles are equal if two sides and the included angle of the one are equal respectively to two swfes <m<i tke included anrjte of the other (sas = sas). B OB' C' Hyp. In A ABC and A'B'C', AB=A'B',... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...equal, respectively, to the base and the two adjacent angles of the other, CONCLUSION. Then the two sides and the included angle of the one are equal, respectively, to the two sides and the included angle of the other. Stated in this way, the hypothesis in Proposition... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 246 pages
...respectively, to a leg and the homologous acute angle of the other. 143. 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. 144. Two right triangles are equal if their legs are equal, each to each. 145. In an... | |
 | James Howard Gore - Geometry - 1902 - 266 pages
...triangle. DB + DA + DC>l(AB + BC + AC). PBOPOSITION XIII. THEOREM. 86. Two triangles are equal each to each when two sides and the included angle of the one are equal respectively to tivo sides and the included angle of the other. C C< B A' In the triangles ABC and A'B'O', let AB =... | |
 | Israel Euclid Rabinovitch - Geometry - 1903 - 140 pages
...that any two triangles whose sides are respectively equal to each other are congruent. Theorem 11. — Two triangles are equal when two sides and the included angle of one are respectively equal to two sides and the included angle of the second. The demonstration given... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...Iden. and Z BAD = Z CAD. Const. .-. AADB = A AZX7, §143 are equal if two sides and the included Z of the one are equal, respectively, to two sides and the included Z of the other). (being homologous angles of equal triangles). §128 QED 146. COR. An equilateral triangle... | |
 | Education - 1917 - 906 pages
...thought. The student is, as a rule, not much surprised to find that two plane triangles are congruent when two sides and the included angle of the one are equal, respectively, to the corresponding parts of the other. On the other hand we really open up broad and surprising vistas... | |
 | Wisconsin. Department of Public Instruction - Education - 1906 - 124 pages
...bisector of an angle is the locus of points equally distant from the sides. 31. Two parallelograms are equal when two sides and the included angle of...equal respectively to two sides and the included angle of the other. 32. The opposite sides of the parallelogram are equal, as are 33. A quadrilateral having... | |
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