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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.
संबंधित प्रश्न
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- Mark the point Q, in your construction, which would make ΔQBC equal in area to ΔABC, and isosceles.
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The locus of a point in rhombus ABCD which is equidistant from AB and AD.
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i) complete the rectangle ABCD such that:
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Ruler and compasses 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 a ΔABC, in which BC = 6 cm, AB = 9 cm and ∠ABC = 60°.
(ii) Construct the locus of the vertices of the triangles with BC as base, which are equal in area to ΔABC.
(iii) Mark the point Q, in your construction, which would make ΔQBC equal in area to ΔABC, and isosceles.
(iv) Measure and record the length of CQ.
