Q. 115.0( 1 Vote )

The figure formed A. Square

B. Rhombus

C. Trapezium

D. None of these

Answer :

Given: ABCD is a rectangle and P, Q, R, S are their midpoints

To Prove: PQRS is a rhombus


Proof: In ABC,


P and Q are the mid points


So, PQ is parallel AC


And,


PQ = AC (The line segment joining the mid points of 2 sides of the triangle is parallel to the third side and half of the third side)


Similarly,


RS is parallel AC


And,


RS = AC


Hence, both PQ and RS are parallel to AC and equal to AC.


Hence, PQRS is a parallelogram


In triangles APS & BPQ,


AP = BP (P is the mid-point of side AB)


PAS = PBQ (90o each)


AS = BQ (S and Q are the mid points of AD and BC respectively and since opposite sides of a rectangle are equal, so their halves will also be equal)


APS BPQ (By SAS congruence rule)


PS=PQ (By c.p.c.t.)


PQRS is a parallelogram in which adjacent sides are equal.


Hence, PQRS is a rhombus.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Newton's Second LawNewton's Second LawNewton's Second Law46 mins
Properties of TrianglesProperties of TrianglesProperties of Triangles54 mins
Law of GravitationLaw of GravitationLaw of Gravitation40 mins
The Last BargainThe Last BargainThe Last Bargain37 mins
The Ant and the CricketThe Ant and the CricketThe Ant and the Cricket4 mins
R D Sharma | Surface Area and VolumesR D Sharma | Surface Area and VolumesR D Sharma | Surface Area and Volumes39 mins
Surface Area and Volume of Right Circular ConeSurface Area and Volume of Right Circular ConeSurface Area and Volume of Right Circular Cone37 mins
Smart Revision | Surface Areas and Volume of SolidsSmart Revision | Surface Areas and Volume of SolidsSmart Revision | Surface Areas and Volume of Solids31 mins
Newton's First LawNewton's First LawNewton's First Law45 mins
Significance of Newton's Laws in daily lifeSignificance of Newton's Laws in daily lifeSignificance of Newton's Laws in daily life42 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses