Question

Construct triangle with sides 5 cm, 4 cm, and 6 cm. Then construct another triangle whose sides are $\frac{2}{3}$ times the corresponding sides of triangle

Answer 1

Step 1

Draw a line segment AB = 4 cm. taking point A as centre, draw an arc of 5 cm radius.

Similarly, taking point B as its centre, draw an arc of 6 cm radius. These arcs will intersect each other at point C. Now, AC = 5 cm and BC = 6 cm and $\Delta ABC$ is the required triangle.

Step 2

Draw a ray AX making an acute angle with line AB on the opposite side of vertex C.

Step 3

Locate 3 points $A_1,A_2,A_3$ (as 3 is greater between 2 and 3) on line AX such that

$A{A}_1=A_1{A}_2=A_2{A}_3$.

Step 4

Join $B{A}_3$ and draw a line through $A_2$ parallel to $B{A}_3$ to intersect AB at point B'.

Step 5

Draw a line through B' parallel to the line BC to intersect AC at C'.

$\Delta A{B}^{\prime }{C}^{\prime }$ is the required triangle.