Draw parallelogram ABCD with the following data:A B=6 cm , A D=5 … - Vidyadip

Question

Draw parallelogram $\text{ABCD}$ with the following data:$A B=6 \ cm , A D=5 \ cm$ and $\angle D A B=45^{\circ}$.Let $A C$ and $D B$ meet in $O$ and let $E$ be the mid$-$point of $B C$. Join $O E$.Prove that:$(i) OE \| AB;(ii) OE =\frac{1}{2} AB$.

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Answer

To draw the parallelogram follows the steps:
$1.$ First, draw a line $A B$ of measure $6 \ cm$. Then draw an angle of measure $45^{\circ}$ at point $A$ such that $\angle D A B=45^{\circ}$ and $A D=5 \ cm$.
$2.$ Now draw a line $C D$ parallel to the line $A B$ of measure $6 \ cm$. Then join $BC$ to construct the parallelogram as shown below:

$3.$ Now it is given that $E$ is the mid-point of $BC$. We join $OE$. Now we are to prove that $OE \| AB$ and $OE =\frac{1}{2} AB$.

$4.$ Since $O$ is the mid$-$point of $A C$ and $E$ is the midpoint of $B C$, therefore the line is parallel to $A B$ and $O E=\frac{1}{2} A B$

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