 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'.  The Elements of Solid Geometry - Page 94by William C. Bartol - 1893 - 95 pagesFull view - About this book
 | Edward Albert Bowser - Geometry - 1891 - 424 pages
...angles are complementary. Proposition 21. Theorem. 104. Two triangles are equal when two sides and tht included angle of the one are equal respectively to two sides and the included angle of the other. Hyp. Let ABC, DEF be two As, having AB = DE, AC = DF. ZA=ZD. To prove A ABC = A DEF.... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...respectively to a side and homologous acute angle of the other. 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. 151. Cor. Two right triangles are equal if their legs are equal, each to each. 152. If... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...three sides of the triangle. / ' v \ DB + DA + DC>\(AB + BC + AC). B C PROPOSITION XIII. THEOREM. 86. Two triangles are equal in all respects when two sides and the included angle of the one are equal reflectively to two sides and the included angle of the other. C B A' In the triangles ABC and A'B'C',... | |
 | Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...Review Prop. I. (Quote it.) Hereafter we can prove that two triangles are equal by • showing that two sides and the included angle of the one are equal respectively to two sides and the included angle of the other, and then quoting Prop. I.; eg, if we have given: (1) The square ABCD, (2) AM = BN, we... | |
 | James Howard Gore - Geometry - 1899 - 266 pages
...DB+ DA + DC>\(AB+ BC+AC). B ^ C PROPOSITION XIII. THEOREM. 86. Two triangles are equal each to each when two sides and the included angle of the one are...equal respectively to two sides and the included angle of the other. C C' B A' In the triangles ABC and A'B'C', let AB = A'B', AC^ A'C', To prove that the... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 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... | |
 | George Albert Wentworth - Geometry - 1899 - 500 pages
...transversal are supplementary. PROPOSITION XXXVII. THEOREM. 185. Two parallelograms 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. In the parallelograms ABCD and A'B'C'D', let AB be equal to AB , AD to A'D', and angle... | |
 | James Howard Gore - Geometry - 1899 - 266 pages
...PROPOSITION XIII. THEOREM. 86. Two triangles are equal each to each when two sides and the inclucted angle of the one are equal respectively to two sides and the included angle of the other. C C' B A' In the triangles ABC and A'B'C", let AB = A'B', AC= A'C', ZA = ZA'. To prove... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...AD, Iden. and Z BAD = Z CAD. Const. .-.AADB = AADC, §143 are eguaZ i/ too sides and the included Z of the one are equal, respectively, to two sides and the included /. of the other). .-.ZB = AC, §128 (being homologous angles of equal triangles'). QED 146. COR. An... | |
 | George Albert Wentworth - Geometry - 1899 - 498 pages
...CB'B. Ax. 2 Hence, Z ABC = ^AB'C. .-.AABC=AAB'C, §143 (two A 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). 38 TRIANGLES. PROPOSITION XXV. THEOREM. 151. Two right triangles are equal if a leg... | |
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