Practical Geometry Test - 2

The given information is not sufficient to draw parallelogram MATH, where MA = 5.6 cm and AT = 4.8 cm.

We need at least one angle or the two diagonals to construct the parallelogram.

i) Angle between the diagonals of a square is 90°, and can never be 70°.
ii) Diagonals of a rectangle are equal.
iii) Only a parallelogram can be formed as the diagonals of a parallelogram are not equal, and they bisect each other.
iv) Diagonals of a rhombus are perpendicular bisectors and the angle between them cannot be 70°.

In case of a kite, we know that adjacent sides are equal and opposite sides are unequal.
Using the above property, we can say that we can't draw a kite using the given data.

It is given that:
i) AB = CD
ii) AB ≠ BC and AD ≠ CD
So, both statements (B) and (D) are correct.

To construct a quadrilateral, the lengths of the four sides and one of the diagonals should be known.
So, both (1) and (2) are necessary.

All the angles of a square are 90°.
All sides of a square are equal. So, with the help of one side's length, we can construct the square.
If we have the diagonal's length, we can calculate the side of the square and easily construct the square.

Five measurements can determine a quadrilateral uniquely.

Possibilities:
1) A quadrilateral can be constructed uniquely if the lengths of its four sides and a diagonal are given.
2) A quadrilateral can be constructed uniquely if the lengths of its two diagonals and three sides are known.
3) A quadrilateral can be constructed uniquely if the lengths of two adjacent sides and three angles are known.
4) A quadrilateral can be constructed uniquely if the lengths of its three sides and two included angles are given.