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Question:

Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are 3/4 of the corresponding sides of the triangle ABC.

Solution:

Constructing △ABC:
Step 1: Draw base BC of length 6 cm using a ruler.
Step 2: Draw a ray from point B at an angle of 60°.
Step 3: Mark an arc of radius 5 cm on the ray is drawn from B and label the intersection point as A. Join A−C. △ABC is the given triangle.

Constructing △EBD with sides 3/4 times the sides of △ABC
Step 1: Draw a ray BX on the opposite side of A.
Step 2: Mark 4 equidistant points B1, B2, B3, B4 on ray BX
Step 3: Join B4 to point C.
Step 4: Draw B3D parallel to B4C and mark the intersection point with line BC as D.
Step 5: Draw DE parallel to CA and mark the intersection point with AB as E. △EBD is the required triangle.