Independent measure to construct quadrilateral
Answers
Answer:
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Explanation:
Construct quadrilaterals when four sides and one diagonal is given.
Draw Δ PQR using SSS construction condition.
With P as the centre, draw an arc of radius 5.5 cm.
With R as the centre, draw an arc of radius 5 cm.
S is the point of intersection of the two arcs. ...
PQRS is the required quadrilateral
WE KNOW THAT
A triangle has six elements – 3 sides and 3 angles. To construct a unique triangle, 3 elements out of six elements are required under a certain combination. A quadrilateral has 8 elements – 4 sides and 4 angles. In addition to these elements a quadrilateral has 2 diagonals which play an important role in determining the size and shape of a quadrilateral. Thus a quadrilateral has 10 elements (4 sides, 4 angles and 2 diagonals) or measurements.
CONSTRUCTING A QUADRILATERAL
To construct a unique quadrilateral we need to know 5 measurements (elements).
Note: To construct a unique quadrilateral simply the knowledge of any five elements is not sufficient. We will need to know a combination of specific 5 elements.
VARIOUS COMBINATIONS OF ELEMENTS FOR CONSTRUCTING A UNIQUE QUADRILATERAL
With the help of the following measurement we can construct quadrilaterals.
(i) Four sides and a diagonal.
(ii) Three sides and two diagonals.
(iii) Four sides and an angle.
(iv) Three sides and two included angles.
(v) Two adjacent sides and three angles.
(vi) Using special properties of a square or a rhombus, etc.