...of the other sides. The figure will suggest the demonstration, which is based on the fact that any side of a triangle is less than the sum of the other two. F,0 474. 923. Theo. — The difference between the distances from two points on opposite sides of a...

...follow that ZA = ZC, and from the second that ZA < ZC, and both are in opposition to what was given. 39. One side of a triangle is less than the sum of the other two. Make ED = BC, then x = y, therefore Z ACD > /.x, but from that it follows (38) that AD > AC, orAB+BC>AC....

...that Z A = Z C, and from the second that Z ^4 < ZC, and both are in opposition to what was given. 39. One side of a triangle is less than the sum of the other two. Make ED = BO, then x = y, therefore /L ACD > Z a;, but from that it follows (38) that AD > AC, or .45+...

...which treats of plane figures — figures whose points are all in the same plane. THEOREM III. Any side of a triangle is less than the sum of the other two, and greater than their difference. 0 Let ABC be any triangle; then: First: Any side will be less than...

...the included angle equal, each to each. THEOREMS RELATING TO LENGTHS AND DISTANCES. 61. Theorem. Each side of a triangle is less than the sum of the other two sides, and greater than their difference. 62. Theorem. The sum of two straight lines, drawn from a...

...opposite the exterior angle, are called the two opposite interior angles, as AA and С. 96. Any nide of a triangle is less than the sum of the other two sides. Since a straight line is the shortest distance between two points, A С < AB + B С. 97. Any...

...: Postulate, theorem, corollary, scholium, axiom. 3. Give the first four axioms of Rue; lid. 4. Any side of a triangle is less than the sum of the other two. 5. From a point within a straight line, only one perpendicular can be drawn. 6. If one side of a triangle...

...the included angle equal, each to each. THEOREMS RELATING TO LENGTHS AND DISTANCES. 61. Theorem. Each side of a triangle is less than the sum of the other two sides, and greater than their difference. 62. Theorem. The sum of two straight lines, drawn from a...

...the included angle equal, each to each. THEOREMS RELATING TO LENGTHS AND DISTANCES. 61. Theorem. Each side of a triangle is less than the sum of the other two sides, and greater than their difference. 62. Theorem. The sum of two straight lines, drawn from a...

...line drawn from the vertex of a triangle to the middle point of the base is called a median. 97. Any side of a triangle is less than the sum of the other two, and greater than their difference. 98. The sum of the three angles of a triangle is equal to two right...