Construct a triangle of sides 4 c m , 5 c m and 6 c m and then a triangle similar to it whose sides are 2 3 of the corresponding sides of the first triangle.

Steps of construction: 1) Draw a Δ A B C such that B C = 4 cm , A C = 5 cm and A B = 6 cm . 2) Draw a ray B X making an acute angle ∠ C B X . 3) Mark three points X 1 , X 2 , X 3 on B X such that B X 1 = X 1 X 2 = X 2 X 3 . 4) Join X 3 C . 5) Draw a line through X 2 such that it is parallel to X 3 C and meets B C at C . 6) Draw a Line through C ' parallel to C A to intersect B A at A ' . Thus, A ' B C ' is the required triangle.

Draw a line segment of length 7 . 6 cm and divide it in the ratio 5 : 8 .

Steps of construction: Draw segment A B of length 7 . 6 cm using a ruler. Draw a ray A C having an acute angle with line A B . Mark 13 equidistant points on ray A C , A 1 , A 2 , A 3 , . . . A 13 . Join A 13 to B . Draw A 5 P parallel to A 13 B . Thus, point P divides A B in the ratio 5 : 8 . Measuring the lengths, we get A P = 2 . 9 cm and P B = 4 . 7 cm .

Construct a triangle of sides 4 c m , 5 c m and 6 c m and then a triangle similar to it whose sides are 2 3 of the corresponding sides of the first triangle.

Steps of construction: 1) Draw a Δ A B C such that B C = 4 cm , A C = 5 cm and A B = 6 cm . 2) Draw a ray B X making an acute angle ∠ C B X . 3) Mark three points X 1 , X 2 , X 3 on B X such that B X 1 = X 1 X 2 = X 2 X 3 . 4) Join X 3 C . 5) Draw a line through X 2 such that it is parallel to X 3 C and meets B C at C . 6) Draw a Line through C ' parallel to C A to intersect B A at A ' . Thus, A ' B C ' is the required triangle.

Draw a triangle A B C with side B C = 6 c m , A B = 5 c m and ∠ A B C = 60 ° .Then construct a triangle whose sides are 3 4 of the corresponding sides of triangle A B C

Steps of construction: ( i ) Draw a line segment B C with measurement of 6 cm . ( ii ) Now construct angle 60 ° from point B and draw A B = 5 cm . ( iii ) Join the point C with point A . Thus △ A B C is the required triangle. ( iv ) Draw a line B X which makes an acute angle with B C and is opposite of vertex A . ( v ) Cut four equal parts of line B X namely B B 1 , B B 2 , B B 3 , B B 4 . ( vi ) Now join B 4 to C . Draw a line B 3 C ' parallel to B 4 C . ( vii ) And then draw a line A ' C ' parallel to A C . Hence, △ A ' B C ' is the required triangle.