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`        ABCD is a quadrilateral  in which P,Q,R,S,are the mid point of the side AB,BC,CD,DA.AC is the diagonal show that pq=sr `
one month ago

Arun
23386 Points
```							Given:In quadrilateral ABCDP,Q,R,S are mid point of sides AB,BC,CD and DA respectivelyT.P: 123In triangle ADC,SR is a line segment joining the mid point of DA and DC respectively:. SR||AC ( mid point therom)In triangle BACPQ is a line segment joining the mid point of BA and BC respectively.PQ||AC (mid point therom)pQ = half of ACFrom 1 &2SR=PQSR ||PQ
```
one month ago
Vikas TU
9810 Points
```							Dear student In ΔABC, P and Q are the mid-points of sides AB and BC respectively.∴ PQ || AC and PQ = 1/2 AC (Using mid-point theorem) ... (1)In ΔADC,R and S are the mid-points of CD and AD respectively.∴ RS || AC and RS = 1/2 AC (Using mid-point theorem) ... (2)From equations (1) and (2), we obtainPQ || RS and PQ = RSSince in quadrilateral PQRS, one pair of opposite sides is equal and parallel toeach other, it is a parallelogram.Let the diagonals of rhombus ABCD intersect each other at point O.In quadrilateral OMQN,MQ || ON ( PQ || AC)QN || OM ( QR || BD)Therefore, OMQN is a parallelogram.⇒ ∠MQN = ∠NOM⇒ ∠PQR = ∠NOMHowever, ∠NOM = 90° (Diagonals of a rhombus are perpendicular to each other)∴ ∠PQR = 90°Clearly, PQRS is a parallelogram having one of its interior angles as 90º.Hence, PQRS is a rectangle.
```
one month ago
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### Course Features

• 31 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions