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प्रश्न
Construct ☐ PQRS, such that l(PQ) = 3.5 cm, l(QR) = 5.6 cm, l(RS) = 3.5 cm, m∠Q = 110°, m∠R = 70°. If it is given that ☐ PQRS is a parallelogram, which of the given information is unnecessary?
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उत्तर
Steps of Construction:
Step 1: Draw PQ = 3.5 cm.
Step 2: Draw ∠PQX = 110°.
Step 3: With Q as the center and a radius of 5.6 cm, draw an arc-cutting ray QX at R.
Step 4: Draw ∠QRY = 70°.
Step 5: With R as centre and radius 3.5 cm, draw an arc cutting ray RY at S.
Step 6: Join PS.
Here, PQRS is the required quadrilateral.
If it is given that quadrilateral PQRS is a parallelogram, then the information l(RS) = 3.5 cm and m∠R = 70° is unnecessary.
संबंधित प्रश्न
The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. Find the measure of each of the angles of the parallelogram.
If the ratio of measures of two adjacent angles of a parallelogram is 1 : 2, find the measures of all angles of the parallelogram.
In the given figure, if points P, Q, R, S are on the sides of parallelogram such that AP = BQ = CR = DS then prove that `square`PQRS is a parallelogram.
ABCD is a parallelogram. What kind of quadrilateral is it if: AC = BD but AC is not perpendicular to BD?
In the following diagram, the bisectors of interior angles of the parallelogram PQRS enclose a quadrilateral ABCD.
Show that:
(i) ∠PSB + ∠SPB = 90°
(ii) ∠PBS = 90°
(iii) ∠ABC = 90°
(iv) ∠ADC = 90°
(v) ∠A = 90°
(vi) ABCD is a rectangle
Thus, the bisectors of the angles of a parallelogram enclose a rectangle.
The given figure shows parallelogram ABCD. Points M and N lie in diagonal BD such that DM = BN.
Prove that:
(i) ∆DMC = ∆BNA and so CM = AN
(ii) ∆AMD = ∆CNB and so AM CN
(iii) ANCM is a parallelogram.
If opposite angles of a quadrilateral are equal, it must be a parallelogram.
A diagonal of a parallelogram bisects an angle. Will it also bisect the other angle? Give reason.
Construct a parallelogram when one of its side is 4 cm and its two diagonals are 5.6 cm and 7 cm. Measure the other side.
Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.
