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Construction

Two line segments AB and AC include an angle of 60° where AB = 5 cm and AC  =  7  cm.  Locate  points  P  and  Q  on AB and AC,  respectively  such  that AP = 3/4 AB and AQ = 1/4 AC . Join P and Q and measure the length PQ.

Construction

Given  a  rhombus  ABCD  in  which  AB  =  4  cm  and ∠ABC = 60°, divide it into two triangles say, ABC and ADC. Construct the triangle AB’C’ similar to ∆ABC with scale factor 2/3  . Draw a line segment C’D’ parallel to CD  where D’ lies on AD. Is AB’C’D’ a rhombus? Give reasons.

Construction

Construct  a  tangent  to  a  circle  of  radius  4  cm  from  a  point  which  is  at  a distance of 6 cm from its centre.

Construction

Draw  a  triangle ABC  in  which  BC  =  6  cm,  CA  =  5  cm  and AB  =  4  cm. Construct a triangle similar to it and of scale factor 5/3. 

Construction

Draw a right triangle ABC in which BC = 12 cm, AB = 5 cm and ∠B = 90°. Construct a triangle similar to it and of scale factor 2/3 . Is the new triangle  also a right triangle? 

Construction

Draw a line segment of length 7 cm. Find a point P on it which divides it in the ratio 3:5.

Construction

Draw an equilateral triangle ABC of each side 4 cm. Construct a triangle similar to it and of scale factor 3/5 . Is the new triangle also an equilateral? 

Construction

Write True or False and give reasons for your answer. 

A pair of tangents can be constructed to a circle inclined at an angle of 170°.

Construction

Write True or False and give reasons for your answer. 

A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of 3 cm from the centre.

Construction

Write True or False and give reasons for your answer. 

To  construct  a  triangle  similar  to  a  given  ∆ABC  with  its  sides 7/3  of  the  corresponding sides of ∆ABC, draw a ray BX making acute angle with BC and X lies on the opposite side of A with respect to BC. The points B₁, B₂, …., B₇ are located at equal distances on BX, B3 is joined to C and then a line segment B6C’ is drawn parallel to B3C where C’ lies on BC produced. Finally, line segment A’C’ is drawn parallel to AC.