Q3 of 805 Page 11

Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are of the corresponding sides of the first triangle.

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, A1,A2,A3,A4, A5,A6,A7( as 7 is greater between 5 and 7), on line AX such that AA1=A1 A2=A2 A3=A3 A4=A4 A5=A5 A6=A6 A7



Step 5: Join BA5 and draw a line through A7 parallel to BA5 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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