Out of three straight lines, which are equal to three given straight lines, to construct a triangle: thus it is necessary that two of the straight lines taken together in any manner should be greater than the remaining one.

In other words, when you construct a triangle, the sum of any two sides must be greater than the remaining one.

Steps:[br]1. Given three straight lines, A, B, and C where the sum of any two are greater than the remaining one.[br][math]A+B>C[/math][br][math]A+C>B[/math][br][math]B+C>A[/math][br]2. Construct a ray DE of sufficient length such that its length is greater than the sum of A, B, and C.[br]3. Define a point F such that DF is equal in length to A (I.3).[br]4. Define a point G such that FG is equal in length to B (I.3).[br]5. Define a point H such that GH is equal in length to C (I.3).[br]6. Draw a circle with center F, and radius DF.[br]7. Draw a circle with center G, and radius GH.[br]8. Draw point K where two circles intersect.[br]9. From the intersection point K, construct two lines KF [br]10. and KG.[br]Therefore out of the three straight lines KF, FG, GK, which are equal to the three given straight lines A, B, C, the triangle KFG has been constructed.[br]Q.E.F.[br][br][br][br]