Name: Rectangles and Squares Formed by Four Points
Uploaded: 2019-07-19
Duration: 6 min 3 s
Description: What are the conditions for a quadrilateral to be a rectangle? How does it differ from a square? Unlock your doubts and clear your basics from this video!

Question

In the adjacent figure

A B ∥ Q P ∥ C D, Q

is the midpoint of

A C .

If

A B = 4 c m

and

C D = 6 c m

then find

P Q .

Accepted Answer

Given figure is:

Here, $A B ∥ Q P ∥ C D$ and $Q$ is the midpoint of $A B = 4 c m$ ,
$A B = 4 c m$ , and $C D = 6 c m$

$A D$ has been joined, such that the line $A D$ intersect $P Q$ at $R$ .

Now, in $Δ A C D, Q$ is the midpoint of $A C$ and $Q R | | C D$ .
$∴$ $R$ is the midpoint of $A D$ . [By mid-point theorem]

And, line segment joining the midpoint of two sides of triangle is half of third side.
$\Rightarrow Q R = \frac{1}{2} C D$ --- $(i)$

Similarly, in $Δ A B D, R$ is the midpoint of $A D$ and $R P | | A B$ .
$∴ P$ is the midpoint of $B D$ , and
$R P = \frac{1}{2} A B$ --- $(i i)$ [ $∵$ Segments joining the midpoint of two sides of a triangle is half of third side]

From equation $(i) and (ii)$ ,
$Q R + R P = \frac{1}{2} (C D) + \frac{1}{2} (A B)$
$\Rightarrow P Q = \frac{1}{2} (C D + A B)$
$\Rightarrow P Q = \frac{1}{2} \times (6 + 4)$
$\Rightarrow P Q = \frac{1}{2} \times 10$
$\Rightarrow P Q = 5 c m$

Therefore, the length of $PQ$ is $5 cm$ .

In the adjacent figure $A B ∥ Q P ∥ C D, Q$ is the midpoint of $A C .$ If $A B = 4 c m$ and $C D = 6 c m$ then find $P Q .$

Important Questions on Quadrilaterals

Learn and Prepare for any exam you want !

In the adjacent figure AB∥QP∥CD, Q is the midpoint of AC. If AB=4 cm and CD=6 cm then find PQ.

Important Questions on Quadrilaterals

Learn and Prepare for any exam you want !

In the adjacent figure $A B ∥ Q P ∥ C D, Q$ is the midpoint of $A C .$ If $A B = 4 c m$ and $C D = 6 c m$ then find $P Q .$