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1. Construct a quadrilateral ABCD when AB = 4 cm, BC = 6 cm, CD = 5 cm, AD = 5.5 cm and AC = 7 cm.

First of all make a rough sketch. Do not start construction without drawing a rough sketch showing sides, angles and diagonals, etc., with correct name.
Step I. Draw a rough sketch and mark the measurements.
Step II. Draw AC = 7 cm.
Step III. With A as centre and radius 4 cm, draw an arc above AC.
Step IV. With C as centre and radius 6 cm, draw another arc intersecting the previous arc at B.
Step V. With centre A and radius 5.5 cm, draw an arc below AC.
Step VI. With centre C and radius 5 cm, draw another arc to intersect the previous arc at D.
Step VII. Join DA and DC.

First of all make a rough sketch. Do not start construction without d

Thus, ABCD is the required quadrilateral.

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Short Answer Type

2. Arshad has five measurements of a quadrilateral ABCD. These are AB = 5 cm, ∠A = 50°, AC = 4 cm, BD = 5 cm and AD = 6 cm. Can he construct a unique quadrilateral? Give reasons for your answer.

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3. We saw that 5 measurements of a quadrilateral can determine a quadrilateral uniquely. Do you think any five measurements of the quadrilateral can do this?

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4. Can you draw a parallelogram BATS where BA = 5 cm, AT = 6 cm and AS = 6.5 cm? Why?

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5. Can you draw a rhombus ZEAL where ZE = 3.5 cm, diagonal EL = 5 cm? Why?

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6. A student attempted to draw a quadrilateral PLAY where PL = 3 cm, LA = 4 cm, AY = 4.5 cm, PY = 2 cm and LY = 6 cm, hut could not draw it. What is the reason?

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