Final answer:
To order the side lengths of IK, KL, IJ, IL, and LJ, one typically uses the Pythagorean theorem or trigonometry, applying them to right triangles. The actual ordering requires specific details from provided figures which are not available here.
Step-by-step explanation:
Ordering Side Lengths in a Triangle
Without the specific lengths or figures referenced in the student's question, it is impossible to accurately order the side lengths of IK, KL, IJ, IL, and LJ. Typically, we would apply the Pythagorean theorem or trigonometry to relationships within right triangles to find these lengths. If the information about the triangles includes side lengths or angles, the Pythagorean theorem can determine the missing side in a right triangle, while trigonometry could be used if angles and at least one side length are known. For vectors, we would compare magnitudes and directions using vector addition or trigonometry to find the resultant vector length.
Since the specific details from the figures are required to accurately solve this question and they are not provided here, you should refer to the actual figures in your textbook or provided resources to find these measures. Examine right triangles separately, and remember that the hypotenuse is the longest side of a right triangle, with the two other sides varying depending on the angles.