 | United States. War Department - 1903 - 446 pages
...а^+1 — 6а:— 6а^+lSжi— 15а¿— 20ж* GEOMETRY. .7. Theorem.— If two sides of a triangle are unequal, the angles opposite are unequal, and the greater angle is opposite the greater side. 3. Problem. — Upon a given straight line, to describe a segment of a circle in which a given angle... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...remaining angles ? 40 TRIANGLES. 41 PROPOSITION XXVII. THEOREM. 153. RECIPROCALLY : If two angles of a triangle are unequal, the sides opposite are unequal,...and the greater side is opposite the greater angle. In the triangle ACB, let the angle C be greater than the angle B. To prove that AB > AC. Proof. Now... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...triangle * of an obtuse triangle ? PROPOSITION XV. THEOREM (CONVERSE OP PROP. XIV) 106. // two angles of a triangle are unequal, the sides opposite are unequal,...and the greater side is opposite the greater angle. Siren ZA greater than ZC in the A ABC. To prove BC > AB. Proof. BC either equals AB, or is less than... | |
 | Fletcher Durell - Geometry - 1911 - 553 pages
...triangle ? of an obtuse triangle ? PROPOSITION XV, THEOREM (CONVERSE OP PROP. XIV) 106, If two angles of a triangle are unequal, the sides opposite are unequal,...and the greater side is opposite the greater angle. B Given /.A greater than ZC in the A ABC. To prove EC > AB. Proof. .BO either equals AB, or is less... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
.../.ACH (= /.BCD} is greater than /.BAC. QED PROPOSITION XIV. THEOREM 104. If two sides of a triangle are unequal, the angles opposite are unequal, and the greater angle is opposite the greater side Given the side BC > side AB in the A ABC. To prove Z BA C greater than Z C. Proof. On the side BC take... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...How many degrees in each of the other two angles ? PROPOSITION XXIII. THEOREM 180 If two angles of a triangle are unequal, the sides opposite are unequal,...and the greater side is opposite the greater angle. HYPOTHESIS. In the A ABC, Z ABC > Z C. CONCLUSION. AC is greater than AB. PROOF Suppose BD drawn making... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...How many degrees in each of the other two angles ? PROPOSITION XXIII. THEOREM 180 If two angles of a triangle are unequal, the sides opposite are unequal,...and the greater side is opposite the greater angle. HYPOTHESIS. In the A ABC, Z ABC > Z C. CONCLUSION. AC is greater than AB. PROOF Suppose BD drawn making... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...(?) (757). And AB is the supplement of Z C', and AC of Z B' (?). .=C' SOLID GEOMETRY 771. THEOREM. If two angles of a spherical triangle are unequal,...and the greater side is opposite the greater angle. Given : A ABC ; Z ABC > Z C. To Prove: AC > AB. Proof : Suppose BR, the arc of a great circte, drawn,... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...... AR + CR > AB (Ax. 6). That is, AC > AB. QED 772. THEOREM. If two sides of a spherical triangle are unequal, the angles opposite are unequal and the greater angle is opposite the greater side. To Prove : Z ABC > Z C. Proof : Z ABC is either < ZC or = ZC or > Z C. Continue by method of exclusion... | |
 | Webster Wells - Geometry - 1908 - 336 pages
...and Z B' = Z C". (§ 560) is sup. of Z C', undAC of Z B' (§ 545), 3. Since PROP. XXI. THEOREM 563. If two angles of a spherical triangle are unequal,...the sides opposite are unequal, and the greater side lies opposite the greater angle. Given, in spherical A ABC, ZABC >Z(7. To Prove AC > AB. PROP. XXII.... | |
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If two angles of a spherical triangle are unequal, the sides opposite are unequal,, and the greater side is opposite the greater angle... 
