Final answer:
To prove that XYK is congruent to LMK, we can use the midpoint theorem. The use of the midpoint theorem is essential to demonstrate the congruence of XYK and LMK, providing a valid proof for the equality between these geometric entities.
Step-by-step explanation:
To mark the diagram, draw a line segment XY and a line segment LM. Then, mark a point K on the line segment XL such that K is the midpoint. Next, draw a line segment YK and a line segment KM.
To prove that XYK is congruent to LMK, we can use the midpoint theorem. The midpoint theorem states that if a line segment has a midpoint, then the line segment can be divided into two congruent segments. Since K is the midpoint of XL, we know that XK is congruent to KL. Additionally, we are given that YK is congruent to KM. Therefore, we have XYK congruent to KLY and YKM congruent to MKL.