State true or false:

A quadrilateral can be constructed uniquely if three angles and any two sides are given.

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True

False

answer is B.

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Detailed Solution

Given a statement, a quadrilateral can be constructed uniquely if three angles and any two sides are given.
We need to find whether the given statement is true or false.
For any quadrilateral to be constructed, at least 5 measurements are necessary.
These are as follows,
4 sides and 1 diagonal
3 sides and 2 diagonals
3 sides and two interior angles
2 adjacent sides and three angles
Now, in the given statement, it is said that if any two sides and three angles are known, then a quadrilateral can be constructed.
This is wrong, as the two side lengths given must be of adjacent sides.
If the side lengths are of opposite sides, then the quadrilateral will be impossible to construct.
Hence, the given statement is false.
Hence, the correct option is (2).

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