Question

Construct a triangle of sides $4cm,5cm$ and $6cm$ and then a triangle similar to it whose sides are $\frac{2}{3}$ of the corresponding sides of the first triangle.

Answer 1

Making the triangle.

• Draw a line segment AB = $4$ cm
• Draw an arc at 5 cm from point A.
• Draw an arc at 6 cm from point B so that it intersects the previous arc.
• Joint the point of intersection from A and B.
• This gives the required triangle ABC.

Dividing the base in $2:3$ ratio:

• Draw a ray AX at an acute angle from AB.
• Plot three points on AX so that; AA1 = A1A2 = A2A3
• Join A3 to B.
• Draw a line from point A2 so that this line is parallel to A3B and intersects AB at point B’.
• Draw a line from point B’ parallel to BC so that this line intersects AC at point C’.

Triangle AB’C’ is the required triangle.