A B C D is a rectangle & PQRS are the mid point of sides A B, B C, CD, D A respectively. Show that P Q R S is a Rohombus
Answers
Answered by
0
Answer:. Let us join AC and BD.
In ΔABC,
P and Q are the mid-points of AB and BC respectively.
∴ PQ || AC and PQ = AC (Mid-point theorem) ... (1)
Similarly in ΔADC,
SR || AC and SR = AC (Mid-point theorem) ... (2)
Clearly, PQ || SR and PQ = SR
Since in quadrilateral PQRS, one pair of opposite sides is equal and parallel to
each other, it is a parallelogram.
∴ PS || QR and PS = QR (Opposite sides of parallelogram)... (3)
In ΔBCD, Q and R are the mid-points of side BC and CD respectively.
∴ QR || BD and QR =BD (Mid-point theorem) ... (4)
However, the diagonals of a rectangle are equal.
∴ AC = BD …(5)
By using equation (1), (2), (3), (4), and (5), we obtain
PQ = QR = SR = PS
Therefore, PQRS is a rhombus
plz mark as brainliest
Similar questions