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Loci (Locus and its Constructions) — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsLoci (Locus and its Constructions)4 Marks
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.
(i) Measure ∠BCD
(ii) Locate point P on BD which is equidistant from BC and CD.

✓

Answer


Steps of construction:
(i) Draw a line AB = 6 cm.
(ii) Draw a ray making an angle of 45° with AB.
(iii) With a as centre, draw AD = 6 cm on the ray.
(iv) Draw an angle bisector of angle BAD.
(v) With Bas centre cut an arc BC = 3.6 cm on the angle bisector. (vi) With Das centre cut an arc CD = 5 cm on the angle bisector. ABCD is the required quadrilateral.
(vii) Join BD.
(viii) Draw perpendicular bisectors of CD and BC which meet BD on P. Pis the required point.

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