Question

Divide seg AB of length 7.5 cm into 6 congruent parts.

Answer 1

Seg AB of length 7.5 cm can be divided into 6 congruent parts in the following way.

Steps of Construction:

(1) Draw a segment AB of length 7.5 cm.

(2) Draw a ray AQ at point A on one side of seg AB and draw a ray BP at point B on other side of AB making an acute angle of the same measure with seg BA.

(3) Take any radius and with the tip of the compass at A, mark a point A₁ on AQ.
Now, with the compass point on A₁ and at the same distance as AA_1, mark another point A_2. Similarly, mark four more points A₃, A₄, A₅ and A₆. Keeping the same radius, mark points B_1,B₂,B₃,B_4,B₅ and B₆ on ray BP as done on ray AQ.

(4) Draw the line segments AB₆, A₁B₅, A₂B₄, A₃B₃, A₄B_2,A₅B₁ and A₆B.
They intersect seg AB at the points P, Q, R, S and T respectively.

Hence, seg AB is divided into 6 congruent parts.