Question

Draw a rectangle, mark the midpoints of each side, join these points to form a quadrilateral. Write
the appropriate name for the quadrilateral?​

Answer 1

Answer:

Given quadrilateral ABCD ,P,Q,R,S is the mid point of AB,BC,CD and AC

Join AC

From equation (1) and (2) , We get

RS||PQ and RS=PQ

So PQRS is a parallelogram (Because pair of opposite side of a quadrilateral is equal and parallel)

Answer 2

Answer:

Parallelogram

Step-by-step explanation:

Let the Rectangle is ABCD, mid point of side AB,BC,CD and DA are P, Q,R and S respectively.

The MidPoint theorem is a special case of the basic proportionality theorem of thales. According to mid-point theorem, a line drawn joining the midpoints of the two sides of a triangle is parallel to the third side.

Considering the triangle $\Delta ABC$, we see that line PQ divides side AB and BC into two parts, so by theorem we have

$AC ||PQ$ ...(1)

Now, consider triangle $\Delta ADC$, we see that line RS divides side DC and AD into two parts , so by theorem we have

$RS||AC$  ...(2)

Thus we have,

PQ || RS

Simmilarly, it is easy to show that,

PS || RQ

$\implies$ PQRS is Parallelogram.

#SPJ3