Quant Question Of The Day: 29
[latexpage]
Geometry
RS is quadrilateral whose diagonals make right angle with each other. A new quadrilateral ABCD was drawn by joining the midpoints of sides PQ, QR, RS and PS respectively. Which of the following must be true about the quadrilateral ABCD?
1. ABCD is a Square.
2. ABCD is a Rhombus.
3. ABCD is a Rectangle.
4. Diagonals of ABCD intersect at 90.
ΔPDA and ΔPSQ are similar and AD is half of SQ. {by mid point theorem)
ΔRCB and ΔRSQ are similar and BC is half of SQ.
Hence, AD||BC and AD = BC
Similarly it can be proved that CD||AB and CD = AB.
So, ABCD is a parallelogram.
It is also given that PR is perpendicular to SQ.
By this it can be concluded that all the angles of quadrilateral ABCD are right angle.
Hence ABCD is a rectangle.
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