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Practical Geometry

Long Answer Type

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

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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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Long Answer Type

7. Construct the following quadrilateral:
Quadrilateral ABCD
AB = 45 cm
BC = 5.5 cm
CD = 4 cm
AD = 6 cm
AC = 7 cm

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Short Answer Type

8. Construct the following quadrilateral:
Quadrilateral JUMP
JU = 3.5 cm
UM = 4 cm
MP = 5 cm
PJ = 4.5 cm
PU = 6.5 cm

Steps of construction:
I. Draw a line segments JU = 3.5 cm.
II. With centre at U and radius UP = 6.5 cm, draw an arc.
III. With centre at J and radius = 4.5 cm, draw another arc to intersect the previous arc at P.
IV. With centre at U and radius = 4 cm, draw an arc on the side opposite to that of J.
V. With centre at P and radius = 4 cm, draw another arc intersecting the previous arc at M.
VI. Join PJ, PU, PM and UM.
Thus, JUMP is the required quadrilateral.

Steps of construction:I. Draw a line segments JU = 3.5 cm.II. With