Question

show that the quadrilateral formed by joining the midpoint of the side of a square is also a square.​

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

We have ,

P,Q,R,S are mid points of quadrilateral

Therefore

By mid point theorem

PQ parallel to BD

and PQ=1 BY 2 times BD .......1

Similarly,we can prove that

RS || BD and RS =1 BY 2 times BD.......2

Therefore,from 1 and 2

□PQRS is a rectangle

Therefore angle P= angle Q=90degree....property of rectangle ....A

Now,

In triangle PQR and triangle PRS,

1.angle Q=angle S....angles of rect.

2.PQ=RS.....earlier proved

3.PR=PR ...... Common side

Therefore,by RHS-test of congruence

Triangle PQR= triangle PRS

Therefore

PQ=PS ....CPCT .....B

Therefore,from A and B

□PQRS is a square

Hence proved!