Construct a triangle of sides 4 cm, 5cm and 6cm and then a
triangle similar to it whose sides areof the corresponding
sides of the first triangle.
Give the justification of the construction.
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
ΔABC is the required triangle.
Draw a ray AX making an acute angle with line AB on the opposite
side of vertex C.
Locate 3 points A1, A2, A3 (as 3
is greater between 2 and 3) on line AX such that AA1 =
A1A2 = A2A3.
Join BA3 and draw a line through A2
parallel to BA3 to intersect AB at point B'.
Draw a line through B' parallel to the line BC to intersect AC at
ΔAB'C' is the required triangle.
The construction can be justified by proving that
By construction, we have
∠ABC (Corresponding angles)
In ΔAB'C' and
∠ABC (Proved above)
ΔABC (AA similarity criterion)
In ΔAA2B' and
ΔAA3B (AA similarity
From equations (1) and (2), we obtain
This justifies the construction.
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