...interior 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...

...a-j+flj, a3 + a4 are also in continued proportion; and that the sum of at + ag, a2 + o3, B. 9. Prove that the sum of any two sides of a triangle is greater and the difference less than the third side. State the limiting cases of these two theorems. D is the...

...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...

...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...

...with the perpendicular. 81. A triangle is a portion of a plane bounded by three straight lines. 92. The sum of any two sides of a triangle is greater than the third side. 94. The perpendicular is the shortest line that can be drawn from a given point to a given line. other...

...Given AB any side of the A ABC, and AOBC. To prove AB > A C— BC. Proof. AB + BOAC, Art. 92. (tht 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. (</ equals be subtracted from...

...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 longest side. To...

...more than two equal oblique lines can be drawn from a given point to a given straight line. Prop. 38. The sum of any two sides of a triangle is greater than the third side. Prop. 39. The difference of any two sides of a triangle is less than the third side. Prop. 40. If from...

...centimetres or half-inches in length, internally and externally in the ratio of 5 to 3. Theoretical. 4. Prove that the sum of any two sides of a triangle is greater than the third aide. 5. Prove geometrically that the rectangle under the sum and difference of two lines is equal...

...points.] (Ax. 7) 2. Subtracting AC from both members of the inequality, AB>BC-AO. PROP. XI. THEOREM 63. The sum of any two sides of a triangle is greater than the sum of the lines drawn from any point within the triangle to the extremities of the remaining side....