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) $OE \| AB;(ii)OE =\frac{1}{2} AB$.

✓

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 $O E=\frac{1}{2} A B$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "[5 marks sum]" from Construction of Polygons (Using ruler and compass only)→Construction of Polygons (Using ruler and compass only) — all question types→MATHEMATICS STD 9 question papers→ICSE Board STD 9 question papers→ICSE Board question paper generator→

Similar questions

In $\triangle ABC , DE$ is drawn parallel to $BC$ cutting $AB$ in the ratio $2: 3$. Calculate:$ \text { (i) } \frac{\operatorname{area}(\triangle ADE )}{\operatorname{area}(\triangle ABC )};\text { (i) } \frac{\operatorname{area}(\text {trapezium EDBC})}{\operatorname{area}(\triangle ABC)}$

The marks of $24$ candidates in the subject mathematics are given below:

$45$	$48$	$15$	$23$	$30$	$35$	$40$	$11$
$29$	$0$	$3$	$12$	$48$	$50$	$18$	$30$
$15$	$30$	$11$	$42$	$23$	$2$	$3$	$44$

The maximum marks are $50.$ Make a frequency distribution taking class intervals $0 - 10, 10-20,\dots .......$

Draw frequency polygons for each of the following frequency distribution: $(a)$ using histogram$(b)$ without using histogram

$C.I$	$10 - 30$	$30 - 50$	$50 - 70$	$70 - 90$	$90 - 110$	$110 - 130$	$130 - 150$
$ƒ$	$4$	$7$	$5$	$9$	$5$	$6$	$4$

Draw the graph for the equation given below; hence find the co$-$ordinates of the points where the graph is drawn meets the co$-$ordinates axes:$\frac{2 x+15}{3}=y-1$

In the following, the coordinates of the three vertices of a rectangle $\text{ABCD}$ are given. By plotting the given points; find, in case, the coordinates of the fourth vertex:$A(2, 0), B(8, 0)$ and $C(8, 4).$

Construct a rectangle $\text{ABCD}$, when $AD = 3.2\ cm$ and diagonal $BD = 5.5\ cm$. Measure $CD.$

If $\sec A = \sqrt{2}$ , find :$\frac{3 \cot ^2 A +2 \sin ^2 A }{\tan ^2 A -\cos ^2 A }$.

A dealer marks his goods $25\%$ above the cost price and then allows $10\%$ discount on it. What is the cost price of an article on which he gains $Rs. 575$?

A straight line is drawn cutting two equal circles and passing through the mid$-$point $M$ of the line joining their centers $O$ and $O'$. Prove that the chords $AB$ and $CD,$ which are intercepted by the two circles, are equal.

A fruit vendor bought $60 \ kg$ of apples at $Rs. 90$ per $kg$. He sold $40 \ kg$ of the apples at a loss of $10\%$. At what per $kg$ should he sell the remaining apples so as to gain $25\%$ on the whole.