Question

ADCD is a rectangle. The points P, Q. R and S arc midpoints of the sides AD, BC, CD and DA respectively. The two axes of symmetry are: (A) AC and BD (D) PR and SQ (C) AC and PR (D) SQ and BD

Answer 1

Join DB and AC such that two triangles ADB and DBC are formed.

We know that the line joining the midpoints of the two sides of triangle is parallel to the third side and is of half the measure of third side.

Here in triangle ADB P and S are the midpoints of AB and AD respectively,hence PS∥DB also PS=

2

1

DB..................1

Similarly,RQ∥DB also RQ=

2

1

DB..................2

PQ∥AC also PQ=

2

1

AC....................3

SR∥AC also SR=

2

1

AC......................4

From equation 1 and 2 we get PS∥RQ and PS=RQ

And from equation 3 and 4 we get PQ∥SR and PQ=SR

Therefore, PQRS is a rhombus.

solution