Q. 2

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

Answer :

Step 1: Draw a line segment AB of 5 cm.

Step 2: Taking A and B as Center, draw arcs of 6 cm and 5 cm radius respectively. Let these arcs intersect each other at point C. △ABC is the required triangle having length of sides as 5 cm , 6 cm , 7 cm respectively.

Step 3: Draw a ray AX making acute angle with line AB on the opposite side of vertex C.

Step 4: Locate 7 points, A_{1},A_{2},A_{3},A_{4,} A_{5},A_{6},A_{7}( as 7 is greater between 5 and 7), on line AX such that AA_{1}=A1 A2=A2 A3=A3 A4=A4 A5=A5 A6=A6 A7

Step 5: Join BA_{5} and draw a line through A_{7} parallel to BA_{5} to intersect extended line segment AB at point B′.

Step 6: Draw a line through B′ parallel to BC intersecting the extended line segment AC at C′.△AB’C’ is the required triangle.

Justification

∆AB' C'~∆ABCby AAA Similarity Condition

And

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