 | Webster Wells - Geometry - 1908 - 329 pages
...Z (7.47). 6. Then, Z BAC must be > Z B. PROP. XXIV. THEOREM 93. (Converse of Prop. XXIII.) If tioo angles of a triangle are unequal, the sides opposite are unequal, and the greater side lies opposite the greater angle. C Draw A ABC having ZBAC>ZB. We then have : Given, in A ABC. Z BAC... | |
 | William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...one equal, respectively, to the three sides of the other). %A, §85 PROPOSITION XXI. THEOREM. 126. If two angles of a triangle are unequal, the sides...and the greater side is opposite the greater angle. Given the A ABC, in which £ CBA > £ C. To prove AC > AB. Proof. Draw BD meeting AC at D and making... | |
 | Geometry, Plane - 1911 - 192 pages
...EXAMINATIONS IN PLANE GEOMETRY FOR ADMISSION TO MASSACHUSETTS INSTITUTE OF TECHNOLOGY JUNE, 1886 1. If two angles of a triangle are unequal, the sides opposite are unequal, the greater side lies opposite the greater angle. 2. If CD is the perpendicular from the vertex of... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...But ^ACB>Zp, Ax. 8 and Zy>ZB. §223 4. • .'. Z.ACB >ZB Axs. 1 and 12 PROPOSITION XXIX. THEOREM 225. If two angles of a triangle are unequal, the sides...and the greater side is opposite the greater angle. Given the triangle ABC, in which angle B is greater than angle C. To prove that AC > A B. Proof. 1.... | |
 | William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...But Z-ACB>Zp, Ax. 8 and Zq>ZB §223 4. .'. Z.ACB > ZB Axs. 1 and 12 PROPOSITION XXIX. THEOREM 225. If two angles of a triangle are unequal, the sides...and the greater side is opposite the greater angle. C >B Given the triangle ABC, in which angle B is greater than angle C. To prove that AC >AB. Proof.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 490 pages
...of the opposite vertices. Thus, in A ABC, AB = c, BC = a, and CA = b. PROPOSITION XXX. THEOREM 130. If two angles of a triangle are unequal, the sides...and the greater side is opposite the greater angle. [Converse of Prop. XXIX.] A Given A ABC, with ZB > Z C. To prove 6 > c. STATEMENTS b < c, or 6 = c,... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...of the opposite vertices. Thus, in A ABC, AB = c, BC = a, and CA = b. PROPOSITION XXX. THEOBEM 130. If two angles of a triangle are unequal, the sides...and the greater side is opposite the greater angle. [Converse of Prop. XXIX.] A Given A ABC, with ZB > Z C. To prove b > c. STATEMENTS b < c, or b = c,... | |
 | Horace Wilmer Marsh - Mathematics - 1914 - 306 pages
...THEOREM 38 Write this theorem as the converse of theorem 37. X THEOREM 39 // two angles of a spherical triangle are unequal, the sides opposite are unequal,...and the greater side is opposite the greater angle. X THEOREM 40 Write this theorem as the converse of theorem 39. X THEOREM 41 The area generated by the... | |
 | Webster Wells, Walter Wilson Hart - Geometry, Plane - 1915 - 330 pages
...158 Ex. 185. If a triangle is scalene, all its angles are unequal. PROPOSITION XXXIV. THEOREM 162. If two angles of a triangle are unequal, the sides opposite are unequal, the side opposite the greater angle being the greater. A Hypothesis. In A ABC, ZC < Z B. Conclusion.... | |
 | William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 pages
...unequal, the angles opposite are unequal, and the greater angle is opposite the greater side. 225. If two angles of a triangle are unequal, the sides...and the greater side is opposite the greater angle. 227. Of all lines that can be drawn from a given point to a given line, the perpendicular is the shortest.... | |
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If two angles of a triangle are unequal, the sides opposite are unequal, and the greater side is opposite the greater angle. 
