SOLUTION: show that the quadrilateral formed by joining the mid-points of the sides of a square is also a square.

Question 161720: show that the quadrilateral formed by joining the mid-points of the sides of a square is also a square.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Given:
, , and are theof , , and respectively.
To prove:
is .
Proof:
Consider triangle
|| and �.(1)
(In a triangle the segment joining the mid-points of
two sides are parallel and equal to third side)
Consider triangle ,
|| and �.(2)

From (1) and (2),
|| and
is a parallelogram ��.(3)
�.. (opposite sides of a rectange)
So
�..
i.e.
Consider triangle , and triangle ,
�. ( is the mid-point of )

angle = =
So, is to triangle .... ( congruency condition)

��..(4)
From (3) and (4),
is a parallelogram in which .
is a .

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