Name: Theorems on Quadrilaterals
Uploaded: 2019-07-19
Duration: 1 min 38 s
Description: Let us learn the theorems of a parallelogram, such as equal opposite sides, equal opposite angles and other properties related to diagonals.

Question

What kind of quadrilateral is formed when the mid points of the sides of a kite, are joined.

Accepted Answer

Let us consider the kite $A B C D$ as shown in the figure.

Now consider the midpoints of sides $A B$ $,$ $A D$ $,$ $B C$ and $C D$ as $P, Q, R, S$ respectively.

Let us also join $B D$ and $A C$ .

Now in isosceles triangle $△$ $A B D$ as $P$ is midpoint of $A B$ and $Q$ is midpoint of $A D$ ,

$P Q =$ $\frac{1}{2}$ $B D$ and $P Q$ $∥$ $B D$ .

Similarly, in $△$ $B C D$ , $R S =$ $\frac{1}{2}$ $B D$ and $R S$ $∥$ $B D$ ,

Hence, $P Q$ $∥$ $R S$ and $P Q = R S$

Similarly, we can prove that $P R = Q S$ and $P R$ $∥$ $Q S$ .

Now using SSS postulate, we can prove $△$ $A B C$ $\equiv$ $△$ $A C D$ .

And hence, $∠$ $B A C$ $=$ $∠$ $D A C$ .

Therefore, $A C$ is bisector of isosceles triangle $△$ $A B D$ .

Hence, $A C$ $⊥$ $B D$ and $P Q$ $⊥$ $P R$

Hence, the quadrilateral formed when the mid points of the sides of a kite are joined is a rectangle.

What kind of quadrilateral is formed when the mid points of the sides of a kite, are joined.

Important Questions on Parallelograms

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