| 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... | |
| George Albert Wentworth - Geometry, Solid - 1902 - 248 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 the** third side, and their difference is less than the third side. 141. Two right triangles are equal if... | |
| George Albert Wentworth - Geometry - 1904 - 496 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 the** third side, and their difference is less than the third side. B In the triangle ABC, let AC be the... | |
| Walter Nelson Bush, John Bernard Clarke - Geometry - 1905 - 378 pages
...Angles are supplemental. VH. SUMMARY OF PROPOSITIONS IN THE GBOUP ON SUM OF LINES AND MID-JOINS 1. **The sum of two sides of a triangle is greater than the** third side. 2. The sum of two lines drawn from any point within a triangle to the ends of one side... | |
| Education - 1908 - 874 pages
...transversal where the sum of the angles is less. than two right angles." He proves as a theorem that **"the sum of two sides of a triangle is greater than the** third side." Which statement I ask is more clearly self-evident? No one would say that Euclid's parallel... | |
| Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...74.] Ex. 3. Through the midpoint of a line An any oblique line is drawn : PLANE GEOMETRY 75. THEOREM. **The sum of two sides of a triangle is greater than...point within the triangle. Given : P, any point in** lines PA and PC. To Prove : AB + BC > AP + PC. Proof : Extend AP to meet BC at X. AB + BX > AP + PX.... | |
| 1906 - 586 pages
...transversal where the sum of the angles is less than two right angles." He proves as a theorem that **"the sum of two sides of a triangle is greater than the** third side." Which statement I ask is more clearly self-evident? No one would say that Euclid's parallel... | |
| Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...74.] Ex. 3. Through the midpoint of a line AB any oblique line is drawn : PLANE GEOMETRY 75. THEOREM. **The sum of two sides of a triangle is greater than...+ BC > AP + PC. Proof : Extend AP to meet BC at X.** A c AB + BX > AP + PX. (Why:) (Ax. 12.) CX + PX > PC. (Why ?) (Ax. 12.) Add : AB + BX + CX + PX > AP... | |
| Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...74.] Ex. 3. Through the midpoint of a line AB any oblique line is drawn : 1'LANE GEOMETRY 75. THEOREM. **The sum of two sides of a triangle is greater than...the third side, from any point within the triangle.** , B Given : P, any point in A ABC ; lines P^ and PC. To Prove : AB + BC > AP + PC. Proof : Extend AP... | |
| Benjamin Warner Snow - Physics - 1909 - 810 pages
...Vector AB + Vector BC = Vector AC. This may seem at first to violate the proposition in geometry that **the sum of two sides of a triangle is greater than the** third. It must, however, be remembered, that a wider meaning has been given to the sign +, and, therefore,... | |
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