Question

Divide seg CD of length 6.4 cm into 3 congruent parts.

Answer 1

Seg CD of length 6.4 cm can be divided into 3 congruent parts in the following way.
Steps of construction:
(1) Draw a segment CD of length 6.4 cm.
(2) Draw a ray CK at point C on one side of seg CD, making an acute angle with it.
Draw a ray DS at point D on the other side of CD, making an acute angle of the same measure with seg CD.
(3) Take any radius and with the tip of the compass at C, mark a point C₁ on CK.
Now, with the compass point on C₁ and at the same distance as CC₁, mark another point C_2. Similarly, mark C₃. Keeping the same radius, mark points D₁, D₂ and D₃ and on ray DS as done on ray CK.
(4) Draw the line segments CD₃, C₁D₂, C₂D₁ and C₃D.
C₁D₂, C₂D₁ intersect seg CD at the points A and B, respectively.

Seg CD is thus divided into 3 congruent parts: CA, AB, BD.