State true or false:

A rhombus can be constructed, given that one of its sides and one angle are known.

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True

False

answer is A.

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Detailed Solution

Given a statement, a rhombus can be constructed, given that one of its sides and one angle are known.
We need to find whether the given statement is true or false.
A rhombus is a special category of parallelogram wherein, all the sides are equal in measure and the diagonals intersect each other at

90 ∘

.
As far as the interior angles are concerned, for a rhombus, the opposite angles are equal in measure.
Based on these properties, we can say that if one of the sides of a rhombus is known, then the remaining three sides will also be of the same length.
Next, if one of the angles is known, then its opposite angle will also be the same.
Then, we can use the angle sum property of a quadrilateral and determine the remaining two angle measures as they will also be opposite angles and will therefore be equal.
So, using the properties of a rhombus, we will have a sufficient number of known dimensions from the given dimensions.
Thus, a rhombus can easily be constructed if one of its sides and one angle is known.
Hence, the given statement is true.
Hence, the correct option is (1).

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