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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
Describe the locus of vertices of all isosceles triangles having a common base.
Use graph paper for this question. Take 2 cm = 1 unit on both the axes.
- Plot the points A(1, 1), B(5, 3) and C(2, 7).
- Construct the locus of points equidistant from A and B.
- Construct the locus of points equidistant from AB and AC.
- Locate the point P such that PA = PB and P is equidistant from AB and AC.
- Measure and record the length PA in cm.
Plot the points A(2, 9), B(–1, 3) and C(6, 3) on graph paper. On the same graph paper draw the locus of point A so that the area of ΔABC remains the same as A moves.
AB and CD are two intersecting lines. Find a point equidistant from AB and CD, and also at a distance of 1.8 cm from another given line EF.
Describe completely the locus of a point in the following case:
Centre of a ball, rolling along a straight line on a level floor.
Draw and describe the locus in the following case:
The locus of a point in the rhombus ABCD which is equidistant from the point A and C.
Without using set squares or protractor construct a triangle ABC in which AB = 4 cm, BC = 5 cm and ∠ABC = 120°.
(i) Locate the point P such that ∠BAp = 90° and BP = CP.
(ii) Measure the length of BP.
Using a ruler and compass only:
(i) Construct a triangle ABC with BC = 6 cm, ∠ABC = 120° and AB = 3.5 cm.
(ii) In the above figure, draw a circle with BC as diameter. Find a point 'P' on the circumference of the circle which is equidistant from Ab and BC.
Measure ∠BCP.
Use ruler and compasses only for the following questions:
Construct triangle BCP, when CB = 5 cm, BP = 4 cm, ∠PBC = 45°.
Complete the rectangle ABCD such that :
(i) P is equidistant from AB and BC and
(ii) P is equidistant from C and D. Measure and write down the length of AB.
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.
