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Question

# Construct a triangle of sides 4 cm,5 cm and 6 cm and then a triangle similar to it whose sides are 23 of the corresponding sides of the first triangle.

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Solution

## Steps of construction:1. Draw a base BC of length 6 cm.2. Place the pointed end of the compass on B and mark an arc of radius 5 cm. Now, place the pointed end on C and mark an arc of radius 4 cm intersecting with the previous arc. Mark this intersection point as A.3. Join A−B and A−C. △ABC is the first triangle.4. Draw a ray BX from point B on opposite side of A to line BC.5. Mark three equidistant points on ray BX and name them B1,B2 and B3.6. Join B3−C. From B2, draw a line parallel to B3C and let it intersect BC in D. From D draw a line parallel to AC and let it intersect AB in E.△BED is the required similar triangle.

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