 If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.  A Text-book of Geometry - Page 44by George Albert Wentworth - 1888 - 386 pagesFull view - About this book
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...the vertex, is parallel to the base. Proposition 49. Theorem. 60. If two triangles have two sides of one equal respectively to two sides of the other,...first greater than the included angle of the second, the third side of the first is greater than the third side of the second. D Hypothesis. In the A ABC... | |
 | George Albert Wentworth - Geometry - 1899 - 496 pages
...included by a side and the base produced. BOOK I. PLANE GEOMETRY. PROPOSITION XXVIII. THEOREM. 154. If two triangles have two sides of the one equal, respectively,...of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...angle included by a side and the base produced. PROPOSITION XXVIII. THEOREM. 154. If two triangles hace two sides of the one equal, respectively, to two sides...of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...Zc = 60°. .'. &ACD is equilateral (why ?), and AD, half of AB = AC. .-.AB = 2AC. " K Ex. 23. If two triangles have two sides of the one equal, respectively, to two sides of the other, and the angles opposite two equal sides equal, the angles opposite the other two equal sides are equal... | |
 | George Albert Wentworth - Geometry - 1899 - 500 pages
...= 60°. .'. &ACD is equilateral (why ?), and AD, half of AB = AC. .'.AB-2AC. ' •B Ex. 23. If two triangles have two sides of the one equal, respectively, to two sides of the other, and the angles opposite two equal sides equal, the angles opposite the other two equal sides are equal... | |
 | George Albert Wentworth - Geometry, Plane - 1899 - 278 pages
...respectively, to two sides of the other, but the included angle of the first triangle greater tlum the included angle of the second, then the third side of the first is greater than the third side of the second. In the triangles ABC and ABE, let AB be equal to AB,... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...parts are equal.] (§ 66) Again, if we suppose ZA < ZD, BC would be < EF. [If two A have two sides of one equal respectively to two sides of the other, but the included Z of the first > the included Z of the second, the third side of the first is > the third side of the... | |
 | Webster Wells - Geometry - 1899 - 450 pages
...parts are equal.] (§ 66) Again, if we suppose ZA < ZD, BC would be < EF. [If two A have two sides of one equal respectively to two sides of the other, but the included Z of the first > the included Z of the second, the third side of the first is > the third side of the... | |
 | Arthur Schultze - 1901 - 260 pages
...impossibility of all except one. (Compare Props. V and VIII.) PROPOSITION XXX. THEOREM 128. If two triangles have two sides of the one equal respectively...angle of the second, then the third side of the first is greater than the third side of the second. Hyp. In & ABC and A'B'C' AB = A'B'; AC = A'C'; ZA>ZA'.... | |
 | Henry Parker Manning - Geometry, Non-Euclidean - 1901 - 120 pages
...and the greater angle lies opposite the greater side. 4. Theorem. If two triangles have two sides of one equal, respectively, to two sides of the other,...first greater than the included angle of the second, the third side of the first is greater than the third side of the second; and conversely, if two triangles... | |
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