Concept explainers
To prove: Quadrilateral SMPR is a parallelogram.
Explanation of Solution
Given information:The end points of the quadrilateral SMPRare at the circumference of
Concept used:
(a) Side-Angle-Side (SAS) Postulate of Congruency of
(b) If both pair of opposite sides are parallel to each other then the quadrilateral is a parallelogram.
Proof:We can clearly see it in the given diagram that the diagonals SPand RMare also the diameter of
As per Thales’ theorem, “Inscribed
So,
Now, in
By Side-Angle-Side (SAS) Postulate of Congruency of triangles we have,
Then,
Also,
Thus,
Hence, a pair of opposite sides is equal and parallel to each other so the given quadrilateral SMPRis a parallelogram.
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