 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 376 pages
...contradict the hypothesis that angle «> angle c. Therefore AB>BC QED PROPOSITION XXII. THEOREM 78. If two triangles have two sides and the included angle...and the included angle of the other, the triangles arc equal. JB' C' GIVEN — AB, AC, and a, of the triangle ABC respectively equal to A'B', A'C, and... | |
 | Henry W. Keigwin - Geometry - 1897 - 254 pages
...PROBLEM. To construct a square on a given side. PROPOSITION XXVI. THEOREM. 115. If two parallelograms have two sides and the included angle of one equal...two sides and the included angle of the other, the parallelograms are equal. 7 ».D *a FIG. 53. [Superpose, and use Ax. III.] 116. COR. If two rectangles... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 574 pages
...contradict the hypothesis that angle «>angle c. Therefore AB<BC. QED PROPOSITION XXII. THEOREM 70. If two triangles have two sides and the included angle...equal respectively to two sides and the included angle of the othcr, the triangles are equal. C' GIVEN — AB, AC, and a, of the triangle ABC respectively... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 374 pages
...triangle /iCJSf= triangle AC'X. §78 [If two triangles have two sides, and the included angle of the one equal respectively to two sides and the included angle of the other, the triangles are equal.] Hence XC=XC'. Now BC'<BX+XC'. §7 [A straight line is the shortest path between any two of... | |
 | Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 490 pages
...I. (MODEL FOR PUPILS.) /. Theorem. If any two triangles have two sides and the included angle of the one equal respectively to two sides and the included angle of the other, the triangles are equal. //. Given: Д ABC and Л DEF, in which (1) AB = DE, (2) A С = D К, and (3) z BA С = ZED F.... | |
 | Webster Wells - Geometry - 1899 - 180 pages
...§ 600.) PROP. XXII. THEOREM. 602. If two spherical triangles on the same sphere, or equal spheres, have two sides and the included angle of one equal,...respectively, to two sides and the included angle of the other, I. They are equal if the equal parts occur in the same order. II. They are symmetrical... | |
 | Harvard University - Geometry - 1899 - 39 pages
...constructed out of card-board. PLANE GEOMETRY BOOKS I TO V. BOOK I. ANGLES, TRIANGLES, AND PERPENDICULARS. THEOREM I. If two triangles have two sides and the included angle of one respectively equal to two sides and the included angle of the other, the triangles are equal. THEOREM... | |
 | Webster Wells - Geometry - 1899 - 196 pages
...§ 600.) PROP. XXII. THEOREM. 602. If two spherical triangles on the same sphere, or equal spheres, have two sides and the included angle of one equal, respectively, to ttvo sides and the included angle of the other, II. They are symmetrical if the equal parts occur in... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...was to be proved. QEF Quod erat faciendum, wh ich was to be done. BOOK I PROPOSITION I. THEOREM 30. If two triangles have two sides and the included angle...the included angle of the other, the triangles are equal in all respects. Let the A ABC and DEF have AB = DE, BC = EF, and ZB = ZE To Prove the A ABC... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...7. THEOREMS ON THE EQUALITY OF TRIANGLES. Two triangles are identically equal if they have — (1) Two sides and the included angle of one equal, respectively, to two sides and the included angle of the other. § 41. (2) A side and the two adjacent angles of one equal, respectively, to a side and... | |
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If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal. 
