By using ruler and compass only, construct a quadrilateral ABCD in which AB = 6.5 cm, AD = 4 cm and ∠DAB = 750. C is equidistant to from the sides if AB and AD, if also C is equidistant from the points A and B.

By using ruler and compass only, construct a quadrilateral ABCD in which AB = 6.5 cm, AD = 4 cm and ∠DAB = 750. C is equidistant to from the sides if AB and AD, if also C is equidistant from the points A and B.

Following are the steps of Construction:

ML Aggarwal Solutions for Class 10 Chapter 14 Image 45

(i) Construct a line segment

\[AB\text{ }=\text{ }6.5\text{ }cm.\]

(ii) At the point A, construct a ray which makes an angle 75⁰ and cut off

\[AD\text{ }=\text{ }4\text{ }cm.\]

(iii) Construct the bisector of ∠DAB.

(iv) Construct the perpendicular bisector of AB which intersects the angle bisector at the point C.

(v) Now join CB and CD.

Hence, ABCD is the required quadrilateral.

i

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