 Each side of a triangle is smaller than the sum of the other two, and greater than their difference. The first part of this theorem is an immediate consequence of the Axiom of Distance (54) ; that is, AC < AB + BC. Subtract AB from both members of this...  Text-book of Elementary Plane Geometry - Page 25by Julius Petersen - 1880 - 73 pagesFull view - About this book
 | Charles Davies, William Guy Peck - Electronic book - 1855 - 592 pages
...equal, the opposite angles are equal ; if the three sides are equal, the triangle is equiangular. 2. Anv side is less than the sum of the other two, and greater than their difference. 3. The sum uf the angles is equal to two right angles ; and if any side he produced, the exterior an<jle... | |
 | Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...equal, the opposite angles are equal ; if the three sides arc equal, the triangle is equiangular. 2. Any side is less than the sum of the other two, and greater than their dirlrrcnce. 3. The sum of the angles is equal to two right angles ; and if any sido lit; produced,... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...altitude falls within the triangle. LIMITS OF SIDES. 266. Theorem. — Each side of a triangle is smaller than the sum of the other two, and greater than their difference. The first part of this theorem is an immediate consequence of the Axiom of Distance (54) ; that is,... | |
 | Eli Todd Tappan - Geometry - 1868 - 444 pages
...altitude falls within the triangle. LIMIT8 OF 8IDE8. 266. Theorem — Each side of a triangle is smaller than the sum of the other two, and greater than their difference. The first part of tins theorem is an immediate consequence of the Axiom of Distance (54); that is,... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...altitude falls within the triangle. LIMITS OF SIDES. 266. Theorem — Each side of a triangle is smaller than the sum of the other two, and greater than their difference. The first part of this theorem is an immediate consequence of the Axiom of Distance (54) ; that is,... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...PX). Scholium. In order that the construction may be possible, any one of the given sides must he lens than the sum of the other two, and greater than their difference (BI, P. .VII., S.). PUOBLKM XI. Given, two sides of a triangle, and the angle opposite one of them,... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...(BI, PX). Scholium. In order that the construction may be possible, any one of the given sides must be less than the sum of the other two, and greater than their difference (BI, P. VII., S.), PROBLEM XI. Given, two sides of a triangle, and the angle opposite one of them,... | |
 | Julius Petersen - Geometry, Modern - 1880 - 86 pages
...make £. A = ~^~~C /LB, then DA^BC. (31). 59. To construct a triangle, having given the three sides. when the one side is less than the sum of the other...when they have the three sides respectively equal. B CO. To construct a triangle, having given two sides and the angle contained by them. Mark off the... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...(1), for instance, we have AC - AB < BC; that is, B C> AC - A B. Therefore, any side of a triangle is less than the sum of the other two, and greater than their difference. Note.—In the statement of any theorem, that which is given or aesumed, in order to prove something... | |
 | George Irving Hopkins - 1891 - 210 pages
...vertex of a triangle to the middle point of the base is called a median. 97. Any side of a triangle is less than the sum of the other two, and greater than their difference. 98. The sum of the three angles of a triangle is equal to two right angles. Sug. Consult Theorems 58... | |
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