ABCD is a quadrilateral in which AC I BD, prove that the quadrilateral formed by joining
the mid-points of consecutive sides of the quadrilateral ABCD is a rectangle
Answers
Given : ABCD is a quadrilateral in which AC ⊥ BD,
quadrilateral formed by joining the mid-points of consecutive sides of the quadrilateral ABCD
To Find : prove that Quadrilateral formed is a rectangle
Solution:
ABCD is a quadrilateral in which AC ⊥ BD,
Let say P , Q , R & S are mid points on AB , BC , CD and AD
line joining the mid-point of two sides of a triangle is parallel to third side and equal to half the length of the third side
PQ || AC and PQ = AC/2
Similarly RS || AC and RS = AC/2
=> PQ = RS
and QR || BD , QR = BD/2
PS || BD , PS = BD/2
=> QR = PS
AC ⊥ BD
=> PQ ⊥ QR and PR
RS ⊥ QR and PS
Opposite sides are equal and adjacent sides are perpendicular
Hence PQRS is a rectangle.
QED
Learn More
In the adjoining figure, D, E and F are mid-points of the sides BC, CA ...
brainly.in/question/13857685
In the figure, P and Q are the mid - points of the sides AB and BC of ...
brainly.in/question/13016408