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Questions
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.
- Measure ∠BCD
- Locate point P on BD which is equidistant from BC and CD.
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Solution 1
Steps of construction:
- Draw a line AB = 6 cm.
- Draw a ray making an angle of 45° with AB.
- With A as the centre, draw AD = 6 cm on the ray.
- Draw an angle bisector of angle BAD.
- With B as the centre, cut an arc BC = 3.6 cm on the angle bisector.
- With Das, centre cut an arc CD = 5 cm on the angle bisector. ABCD is the required quadrilateral.
- Join BD.
- Draw perpendicular bisectors of CD and BC which meet BD at P. P is the required point.
Solution 2
- ∠BCD = 62°.
- 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.
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