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

Steps of construction: Construct a △ ABC , where AB = 7 cm , BC = 6 cm and AC = 5 cm . Make an acute angle ∠ BAX below the side AB . Locate seven points (greater of 7 and 5 in 7 5 ). A 1 , A 2 . . . . . . . A 7 such that AA 1 = A 1 A 2 = . . . . . . . . = A 6 A 7 . Join BA 5 . Through A 7 , draw a line parallel to A 5 B , intersecting AB (produced) at A ' such that AB ' = 7 5 AB . Through B ' , draw a line parallel to BC intersecting AC (produced) at C ' . Hence, △ AB ' C ' is the required triangle.

Draw a triangle ABC with BC = 6 cm , AB = 5 cm and ∠ ABC = 60 ° . Then construct a triangle whose sides are 3 4 of the corresponding sides of the triangle ABC .

Given BC = 6 cm , AB = 5 cm and ∠ ABC = 60 ° . Required : To construct a triangle whose sides are 3 4 times the sides of △ ABC . Steps of Construction : Take base BC = 6 cm . Construct an angle of measure 60 ° at B i.e., ∠ CBX = 60 ° . With B as centre and radius = 5 cm , draw an-arc intersecting BX at A ' . Join A and C . Hence, △ ABC is the required triangle. At B , make any acute angle ∠ CBY below BC . Locate four points (greater of 3 and 4 in 3 4 ) B 1 , B 2 , B 3 , B 4 on BY such that BB 1 = . . . . . . = B 3 B 4 . Join B 4 and C . Draw a line through B 3 (smaller of 3 and 4 in 3 4 ) parallel to B 4 C making corresponding angles. Let the line through B 3 intersect BC in C ' . Through C ' ,draw a line parallel to CA intersecting BA in A ' . Hence △ AB ' C ' is the required triangle whose sides are 3 4 of the corresponding sides of △ ABC .