| Royal Military Academy, Woolwich - Mathematics - 1909 - 456 pages
...XYZW have AB = XY, BC= YZ, CD = ZW, B= Y, C = Z. Show that they are equal in every respect. 2. Show **that any two sides of a triangle are together greater than the third.** Give in substance the enunciation of propositions from which you know that the sum of the squares on... | |
| Herbert Spencer - Philosophy - 1910 - 780 pages
...it falls within or without some other; and the like. Let us take as an example the proposition — " **Any two sides of a triangle are together greater than the third side."** " Let ABC be a triangle ; any two sides of it are, together, greater than the third side; namely, BA,... | |
| Alexander H. McDougall - Geometry - 1910 - 316 pages
...of the bisectors to the vertex of the third ^ of the A bisects that third Z. INEQUALITIES THEOREM 16 **Any two sides of a triangle are together greater than the third side.** B DC Hypothesis. — ABC is a A. To prove that AB + AC> BC. Construction. — Bisect ZA and let the... | |
| Thomas Aloysius O'Donahue - Mine surveying - 1911 - 288 pages
...is, as 12 is to 8. As BC equals 10, EF equals T % of 10 = 6|, and as CA = 8, FD = ^ of 8 = 5 J. X. **Any two sides of a triangle are together greater than the third side.** XL Parallelograms upon the same base or upon equal bases, 8 C Fio. 41. and between the same parallel,... | |
| Alberta. Department of Education - Education - 1911 - 226 pages
..."Indirect Method of Proof" and illustrate it fully by reference to a proposition in Book I. 8 2. (a) **Any two sides of a triangle are together greater than the third side.** 20 — I. 6 (b) The sum of the distances of any point from the three angular points of a triangle is... | |
| William Ernst Paterson - Logarithms - 1911 - 262 pages
...one side be produced the exterior angle equals the sum of the two interior opposite angles. Prop. 7. **Any two sides of a triangle are together greater than the third.** Prop. 8. Two triangles are congruent (ie are equal in every respect) if they have — (a) two sidea... | |
| Queensland. Department of Public Instruction - Education - 1912 - 234 pages
...formed by two intersecting straight lines are two straight lines at right angles to one another. 3. **Any two sides of a triangle are together greater than the third side.** 4. P is a moving point on a fixed line A15 : O is a fixed point outside the lino. P is joined to O,... | |
| George St. Lawrence Carson - Mathematics - 1913 - 154 pages
...of a science may not be a postulate in another. In Euclid's development of geometry, the statement **that any two sides of a triangle are together greater than the third side** is not a postulate, because it is deduced from other statements (postulates) which are avowedly assumed... | |
| Newfoundland Council of Higher Education - 1913 - 228 pages
...of a quadrilateral bisect each other, prove that the quadrilateral is a parallelogram. (15) 2. Prove **that any two sides of a triangle are together greater than the third side.** Show that the diagonals of a quadrilateral are together less than the perimeter of the quadrilateral,... | |
| Queensland. Department of Public Instruction - Education - 1913 - 274 pages
...AC, AE are the perpendiculars from A upon these bisectors. Prove that CE is parallel to BD. 3. Prove **that any two sides of a triangle are together greater than the third.** 4. Two fixed points P and Q are taken, and AB is an unlimited straight line in the same plane as P... | |
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