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" AB>AC-BC: that is, the difference of any two sides of a triangle is less than the third side. "
A Course of Mathematics: In Two Volumes. For the Use of Academies, as Well ... - Page 257
by Charles Hutton - 1818 - 558 pages
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Rational Geometry: A Text-book for the Science of Space; Based on Hilbert's ...

George Bruce Halsted - Geometry - 1904 - 322 pages
...A perpendicular side-bisector which contains a vertex . S. Two congruent angle-bisectors. Ex. 165. The difference of any two sides of a triangle is less than the third side. Ex. 1 66. From the ends of a side of a triangle the two sects to a point within the triangle are together...
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Syllabus of Plane' Geometry: (corresponding to Euclid, Book I-VI) : Prepared ...

Cora Lenore Williams - Geometry - 1905 - 50 pages
...straight line. Prop. 38. The sum of any two sides of a triangle is greater than the third side. Prop. 39. The difference of any two sides of a triangle is less than the third side. Prop. 40. If from a point within a triangle, two lines are drawn to the extremities of a side, their...
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The Elements of Geometry

Walter Nelson Bush, John Bernard Clarke - Geometry - 1905 - 378 pages
...ends of one side is less than the sum of the two other sides of the triangle. a The difference between any two sides of a triangle is less than the third side. 3. If a series of parallels cut off equal segments on one transversal, (a) They will cut off equal...
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A School Geometry, Parts 1-4

Henry Sinclair Hall - 1908 - 286 pages
...angles ABC, ACB respectively : shew that, if AB is greater than AC, then OB is greater than OC. 8. The difference of any two sides of a triangle is less than the third side. 9. The sum of the distances of any point from the three angular points of a triangle is greater than...
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The Ontario High School Geometry: Theoretical

Alexander H. McDougall - Geometry - 1910 - 316 pages
...Similarly it may be shown that AB>BD. .. AB + AC> BD + DC, ie, AB + AOBC. Cor.— The difference between any two sides of a triangle is less than the third side. r ABC is a A. It is required to show that AB - AC < BC. AB < AC + BC. (1—16, p. 59.) From each of...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 490 pages
...taken, then AB + BC> AD + DC. AEx. 306. If from any point E in A ABC EB and EC are drawn, then Ex. 307. The difference of any two sides of a triangle is less than the third side. Ex. 308. A diagonal of a quadrilateral is less than one half the perimeter of the figure. PROPOSITION...
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Schultze and Sevenoak's Plane Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...taken, then AB + BOAD + DC. A Ex. 306. If from any point E in A ABC EB and EC are drawn, then Ex. 307. The difference of any two sides of a triangle is less than the third side. Ex. 308. A diagonal of a quadrilateral is less than one half the perimeter of the figure. PROPOSITION...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...A ABC EB and EC are drawn, then AB + AC>EB + EC. HINT. Produce BE until it meets AC in D. Ex. 307. The difference of any two sides of a triangle is less than the third side. Ex. 308. A diagonal of a quadrilateral is less than one half the perimeter of the figure. PROPOSITION...
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Junior High School Mathematics, Book 1

Edson Homer Taylor, Fiske Allen - Mathematics - 1919 - 244 pages
...x being greater than y, construct 3 x — 2 y. 4. Show by construction that the difference between any two sides of a triangle is less than the third side. 6. A boy makes an error of 2' 8" in measuring the length of a lot which the surveyor says is 180' long....
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Plane Geometry: I. Abridged and Applied. II. College Preparatory

Matilda Auerbach, Charles Burton Walsh - Geometry, Plane - 1920 - 408 pages
...equilateral triangle to the three sides is equal to the altitude. 236 Theorem 21a. The difference between any two sides of a triangle is less than the third side. Hint: If c <a+6, how can we express a in terms of b and c? Theorem 215. // two sides of a triangle...
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