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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?

No, any 5 measurements (elements) cannot determine a quadrilateral. Actually to construct a quadrilateral, we need a specific combination of measurements such as:

(a) Four sides and one diagonal.
or
(b) Three sides and two diagonals.
or
(c) Two adjacent sides and three angles.
or
(d) Three sides and two included angles.
or
(e) Some special properties are given.

No, any 5 measurements (elements) cannot determine a quadrilateral. Ac

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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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