Recall that if three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
See solution.
Practice makes perfect
Let's begin with recalling what we can say about congruent parts of parallel lines using the Three Parallel Lines Theorem.
Three Parallel Lines Theorem
If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
Having this information in mind, let's first construct a segment separated into four congruent segments. We will start with drawing a segment AB, which will be 3 inches long.
Next, we will draw the second segment, AC.
After this, with the compass at A, we will mark off an arc that intersects AC at X.
Using the same compass setting, we will mark off Y,Z, and W such that AX≅XY≅YZ≅ ZW.
The next step will be to connect B and W with a segment.
Finally, we will construct lines through X,Y and Z that are parallel to WB. Label the intersection points on AB as J,K and L.
Since parallel lines cut off congruent segment on transversals, AJ≅JK≅KL≅LB. Therefore, we separated a 3 inch long segment into four congruent segments.
