Question

Without using set squares or protractor, construct a quadrilateral ABCD in which ∠ BAD = 45°, AD = AB = 6 cm, BC= 3.6 cm and CD=5 cm. Locate the point P on BD which is equidistant from BC and CD. 

Without using set squares or protractor, construct a quadrilateral ABCD in which ∠ BAD = 45°, AD = AB = 6 cm, BC = 3.6 cm and CD = 5 cm.

1. Measure ∠BCD
2. Locate point P on BD which is equidistant from BC and CD.

Answer 1

Steps of construction:

1. Draw a line AB = 6 cm. 
2. Draw a ray making an angle of 45° with AB. 
3. With A as the centre, draw AD = 6 cm on the ray. 
4. Draw an angle bisector of angle BAD. 
5. With B as the centre, cut an arc BC = 3.6 cm on the angle bisector. 
6. With Das, centre cut an arc CD = 5 cm on the angle bisector. ABCD is the required quadrilateral. 
7. Join BD. 
8. Draw perpendicular bisectors of CD and BC which meet BD at P. P is the required point. 

Answer 2

1. ∠BCD = 62°.
2. Draw the angle bisector of ∠BCD. Join BD.
   The point of intersection of the bisector and BD is P. P is equidistant from BC and CD.