| 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 - 250 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 - 562 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 - 492 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 - 178 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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