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प्रश्न
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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उत्तर १
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.
उत्तर २
- ∠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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Ruler and compass only may be used in this question. All construction lines and arcs must be clearly shown, and be of sufficient length and clarity to permit assessment.
(i) Construct Δ ABC, in which BC = 8 cm, AB = 5 cm, ∠ ABC = 60°.
(ii) Construct the locus of point inside the triangle which are equidistant from BA and BC.
(iii) Construct the locus of points inside the triangle which are equidistant from B and C.
(iv) Mark as P, the point which is equidistant from AB, BC and also equidistant from B and C.
(v) Measure and record the length of PB.
