Question

Divide seg LM of length 9 cm into 5 congruent parts.

Answer 1

Seg LM of length 9 cm can be divided into 5 congruent parts in the following way.
Steps of construction:
(1) Draw a segment LM of length 9 cm.
(2) Draw a ray LQ at point L on one side of seg LM, making an acute angle and make another angle of the same measure with seg LM at point M and the new ray is MP.
(3) Take any radius and with the tip of the compass at L, mark a point L₁ on LM.
Now, with the compass point on L₁ and taking same distance as L L₁, mark another point L₂. Similarly, mark three more points L₃, L₄ and L₅. Keeping the same radius, mark points M₁, M₂, M₃, M₄ and M₅ on ray MP as done on ray LQ
(4) Draw the line segments LM₅, L₁M₄, L₂M₃, L₃M₂, L₄M₁ and L₅M.
L₁M₄, L₂M₃, L₃M₂, L₄M₁ intersect seg LM at the points A,B ,C and D, respectively.

Seg LM is thus divided into 5 congruent parts: LA, AB, BC, CD, DM.