 | John Bascombe Lock - Logarithms - 1896 - 244 pages
...measured in angular units ; eg c is measured by angle AOB. We know, then, the following properties : 1. * The sum of two sides of a triangle is greater than the third. 2. The greatest side is opposite the greatest angle, and conversely. 3. Any angle A < 180°. 4. (A... | |
 | George Albert Wentworth - Geometry - 1898 - 266 pages
...lines, and angles, similarly situated in equal or similar figures, are called homologous. 137. THEOBEM. The sum of two sides of a triangle is greater than...and their difference is less than the third side. In the A ABC (Fig. 1), AB+BC>AC, for a straight line is the shortest distance between two points ;... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 246 pages
...the triangle. 128. The homologous sides and the homologous angles of equal triangles are equal. 138. The sum of two sides of a triangle is greater than...and their difference is less than the third side. 141. Two right triangles are equal if the hypotenuse and an acute angle of the one are equal, respectively,... | |
 | George Albert Wentworth - Geometry - 1899 - 498 pages
...opposite interior angles, and therefore greater than either of them. PROPOSITION XIX. THEOREM. 138. The sum of two sides of a triangle is greater than...and their difference is less than the third side. A o In the triangle ABC, let AC be the longest side. To prove that AB + BC > AC, and AC - BC < AB.... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...opposite interior angles, and therefore greater than either of them. PROPOSITION XIX. THEOREM. 138. Tlie sum of two sides of a triangle is greater than the...and their difference is less than the third side. a In the triangle ABC, let AC be the longest side. To prove that AB + BOAC, and AC — BC < AB. Proof.... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...EF. (?) CD + DF < CE + EF. (?) .-. 2CD<2CE. (?) .-. CD<CE. (?) QED • Proposition 13. Theorem. 23. The sum of two sides of a triangle is greater than the sum of two lines drawn from a point within the triangle to the extremities of the third side. Hypothesis.... | |
 | Education - 1895 - 812 pages
...be between 0J and 180D. 8. Show that but one angle of a triangle may be 90° or greater. 4 Show that the sum of two sides of a triangle is greater than the third. 5. Given two angles of a triangle to find the third. The above is a fair sample of the method of the... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...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...and their difference is less than the third side. Given. — Let ABC be a triangle. To Prove. — We are to prove that AC+ BC> AB, and also AB BC < AC.... | |
 | Eldred John Brooksmith - Mathematics - 1901 - 368 pages
...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...and their difference is less than the third side. 2. If two quadrilaterals ABCD, EFGH have the four angles A, B, C, D respectively equal to the four... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...EXERCISE. Complete the following table. The polygons are equiangular. PROPOSITION XXVI. THEOREM 168. The sum of two sides of a triangle is greater than the third side, but the difference of two sides of a triangle is less than the third side. B Let ABC be any A. To Prove... | |
| |
The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side. 
