 | Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...shown that AC and CB are together greater than AB, and CB and BA than AC. QED COR. The difference of any two sides of a triangle is less than the third side. *Ex. 1 8. The straight line drawn from the vertex of a triangle to the middle point of the base is... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...away either of the sides AB, BC, as BC, for example, there remains (A. 5), AC - BC < AB ; that is, the difference between any two sides of a triangle is less than the third side. resent the sides of a triangle, the sum of any two must be greater than the third, and the difference... | |
 | Richard Anthony Proctor - Geometry - 1887 - 202 pages
...Section I. and shall see farther on. The following proposition is often useful : — PROP. XIV. — The difference between any two sides of a triangle is less than the third side. From A 0, a side of the triangle ABC, cut off DC equal to B 0 ; then the remainder AD is less than... | |
 | Euclid, John Bascombe Lock - Euclid's Elements - 1892 - 188 pages
...diagonals. 4. The sum of the sides of a quadrilateral is greater tftan the sum of the diagonals. 5. The difference between any two sides of a triangle is less than the third side. 6. Given two points C, D and a straight line AB, find P in AB such that the difference between PC and... | |
 | Euclid - Geometry - 1892 - 460 pages
...that, if AB is greater than AC, then OB is greater than OC. ON PROPOSITION 20. 7. The difference of any two sides of a triangle is less than the third side. 8. In a quadrilateral, if two opposite sides which are not parallel are produced to meet one another;... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...BD, and AD equals BC, and AD and BC intersect at O. Prove tkat AOB is an isosceles triangle. Ex. 60. The difference between any two sides of a triangle is less than the third side. PROPOSITION XXXIII. THEOREM. 108. Converse of Prop.XXXII,!. The shortest lin* from, a point- to a line... | |
 | 1894 - 1136 pages
...bisects the base. What kind of triangle is this? 6. The opposite angles of a rhombus are equal. 7. The difference between any two sides of a triangle is less than the third side. GRAMMAR. NOTE. — Candidates will answer all parts of the first three questions, and any three questions... | |
 | Frederick Coate Wade - Catholic Church Education Manitoba - 1895 - 168 pages
...PROTESTANT SECTION. FIRST CLASS. EUCLID. 1. Any two sides of a triangle are greater than the third side. The difference between any two sides of a triangle is less than the third side. 2. The opposite sides and angles of a parallelogram are equal to one another and the diagonal bisects... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...b>AD. Th. 7. State it 5. Similarly a> DB. 6. .'. a + b>c. Add 4 and 5 COROLLARY. The difference of any two sides of a triangle is less than the third side. For if a + b > c, and c > b, then a > c — b, by ax. 5. EXERCISES. 55. State the converse of each of the... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
....'.b>AD. Th. 7. State it 5. Similarly a> DB. 6. .'.a+b>c. Add 4 and 5 COROLLARY. The difference of any two sides of a triangle is less than the third side. For if a + b > c, and c > b, then a > c — b, by ax. 5. EXERCISES. 55. State the converse of each of the... | |
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The difference between any two sides of a triangle is less than the third side. 
