 | Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 272 pages
...the isosceles triangle ABC " (see figure on p. 28), it is often better to say : PROPOSITION VIII. 75. Theorem. The sum of any two sides of a triangle is greater than the third side. Given theAJ . B(7. To prove that Proof. 1. Suppose Then 2. And a + b > c. Z C bisected by CD. Z CD... | |
 | William James Milne - Geometry - 1899 - 404 pages
...ABC which joins the points A and C. That is, AC is less than AB + BC. Therefore, etc. QED 125. Cor. The sum of any two sides of a triangle is greater than the third side. Ex. 65. May a triangle be formed with lines 4, 2, and 3 inches long ? With lines 6, 1, and 2 inches... | |
 | William James Milne - Geometry, Modern - 1899 - 258 pages
...ABC which joins the points A and C. That is, AC is less than AB + BC. Therefore, etc. QED 125. Cor. The sum of any two sides of a triangle is greater than the third side. Ex. 65. May a triangle be formed with lines 4, 2, and 3 inches long ? With lines 6, 1, and 2 inches... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...middle points of the sides are called the medial lines or medians of the triangle. PROPOSITION XVI. — THEOREM. The sum of any two sides of a triangle is greater than the third side, and their difference is less than the third side. Given. — Let ABC be a triangle. To Prove. — We... | |
 | Euclid - Geometry - 1901 - 672 pages
...them are together greater than the third, we have to remark that it has already been demonstrated that the sum of any two sides of a triangle is greater than the third side. It is therefore that the two circles cut each other. If the sum of A and В be not greater than J,... | |
 | Eldred John Brooksmith - Mathematics - 1901 - 368 pages
...must not violate Euclid's sequence of propositions. Great importance will be attached to accuracy.] 1. The sum of any two sides of a triangle is greater than the third side, and their difference is less than the third side. 2. If two quadrilaterals ABCD, EFGH have the four... | |
 | J. Elliott - Geometry - 1902 - 290 pages
...difference of the other sides. 11. Prove that the diagonals of a rhombus are unequal. 12. Prove that the sum of any two sides of a triangle is greater than twice the median which bisects the third side. [If the median is produced to double its length and... | |
 | 1903 - 898 pages
...opposite angles. Hence show that every triangle must have at least two acute angles. 5. Prove that the sum of any two sides of a triangle is greater than the third side. Prove also that the sum of the three sides of a. triangle is greater than twice the straight line drawn... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...sides. Given AS any side of the A ABC, and AC >BC. To prove AB>AC— BC. Proof. AB + BOAC, Art. 92. (the sum of any two sides of a triangle is greater than the third side). Subtracting BC from each member of the inequality, AB>AC— BC, Ax.9. {if equals be subtracted from... | |
 | Fletcher Durell - Geometry - 1911 - 553 pages
...two sides. Given AB any side of the A ABC, and AOBC. To prove AB>AC—BC. Proof. AB + BO AC, Art. 92. (the sum of any two sides of a triangle is greater than the third side), Subtracting BC from each member of the inequality, AB>AC—BC, Ax. 9. yf equals l)e subtracted from... | |
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America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side. 
