| George Clinton Shutts - 1905 - 260 pages
...bisects the vert'cal angle of an isosceles triangle bisects the triangle. PROPOSITION XL 87. Theorem. Any side of a triangle is less than the sum of the other two. B A Let ABC represent any triangle. To prove that any s'de, as AB, is less than the sum o] the other... | |
| Education - 1911 - 946 pages
...equal angles are equal. [N3.] 12. The bisectors of vertical angles lie in a straight line. [J4-] 13. Any side of a. triangle is less than the sum of the other two and greater than their difference. [*] 1-4. A diameter bisects a circle. [A5.1 15. A straight line... | |
| Education - 1913 - 914 pages
...compare so as to discern the relation of any side to the sum of the other two. II. Fundamental theorems. Any side of a triangle is less than the sum of the other two. III. Dependent theorems. a. If two sides of a triangle are unequal the angles opposite them are unequal,... | |
| Education - 1906 - 958 pages
...adopted.] Your committee beg leave to report as follows : (1) We believe that it is self-evident that one side of a triangle is less than the sum of the other two ; however Euclid 1 : 20 shows that it is not necessary to make this assumption. (2) That the shortest... | |
| Isaac Newton Failor - Geometry - 1906 - 440 pages
...angles of a triangle are 65° and 84° respectively, find the third angle. PROPOSITION XIII. THEOREM 160 Any side of a triangle is less than the sum of the other two sides. HYPOTHESIS. Let AC be the longest side of the triangle ABC. CONCLUSION. AC < AB + BC. PROOF The straight... | |
| Isaac Newton Failor - Geometry - 1906 - 431 pages
...angles of a triangle are 65° and 84° respectively, find the third angle. PROPOSITION XIII. THEOREM 160 Any side of a triangle is less than the sum of the other two sides. HYPOTHESIS. Let AC be the longest side of the triangle ABC. CONCLUSION. AC < AB + BC. PROOF The straight... | |
| Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...to each of two parallels they will be in the same line. [Draw a third II through the point.] 86. One side of a triangle is less than the sum of the other two sides. 87. The sum of the sides of any polygon ABODE is greater than the sum of the sides of triangle A CE.... | |
| Alva Walker Stamper - Geometry - 1906 - 188 pages
...straight line is the shortest path between two points. Boys cross lots without first learning that one side of a triangle is less than the sum of the other two. These facts of nature are used because they are serviceable. The Indian fastened his pony to a stake,... | |
| Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...to each of two parallels they will be in the same line. [Draw a third II through the point.] 86. One side of a triangle is less than the sum of the other two sides. 87. The sum of the sides of any polygon ABCDE is greater than the sum of the sides of triangle A CE.... | |
| Euclid - Mathematics, Greek - 1908 - 550 pages
...OM. Consider the point Jlf, one of those which follow M, such that AfAf is equal to tr. Then, because any side of a triangle is less than the sum of the other two, OM' <OM + MM'. But OM+ MM1 = OM + a- < R, whence OM' < R, which is absurd. A similar absurdity would... | |
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