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. Plane and Solid Geometry - Page 45by Arthur Schultze, Frank Louis Sevenoak - 1902 - 370 pagesFull view - About this book
| 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... | |
| 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... | |
| Henry Parker Manning - Geometry, Non-Euclidean - 1901 - 116 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... | |
| 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... | |
| Henry Parker Manning - Geometry, Non-Euclidean - 1901 - 122 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... | |
| Arthur Schultze - 1901 - 260 pages
...forming the acute angle ADB, which is the greater side, AB or ACf i PROPOSITION XXXI. THEOREM 129. If two **triangles have two sides of the one equal respectively to two sides of the other, but the** third side of the first greater than the third side of the second, then the included angle of the first... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...forming the acute angle ADB, which is the greater side, ABoT AC? PROPOSITION XXXI. THEOREM 129. If two **triangles have two sides of the one equal respectively to two sides of the other, but the** third side of the first greater than the third side of the second, then the included angle of the first... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...forming the acute angle ADB, which is the greater side, ABor AC1 D PROPOSITION XXXI. THEOREM 129. If two **triangles have two sides of the one equal respectively to two sides of the other, but the** third side of the first greater than the third side of the second, then the included angle of the first... | |
| Alan Sanders - Geometry, Modern - 1901 - 260 pages
...Prove A GBH = AHB C. Whence HG = HC. AH + HG>AG. (?) AOAd. (?) AC>DF. (?) QEI> 182. CONVERSE. If two **triangles have two sides of the one equal respectively to two sides of the other,** and the third sides unequal, the included angles are unequal, and the greater included angle belongs... | |
| Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...herelore BC is greater thaii BC'. That is, .#6' is greater than B'C. PROPOSITION XXI \ 80. // £M;G» **triangles have two sides of the one equal, respectively, to two sides of** tlie other, and the third sides unequal, the triangle which has the greater third side has also the... | |
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