[4 marks sum]

Question 14 Marks

Construct a parallelogram $\text{ABCD}$. Given:$AB = 5.5\ cm, BC = 3.5\ cm, \angle B = 75^\circ $

Answer

$AB = 5.5\ cm, BC = 3.5\ cm, \angle B = 75^\circ $

Since opposite sides of a parallelogram are equal;
$AB = DC = 5.5\ cm$ and $BC = AD = 3.5\ cm$
Steps of Construction:
$1)$ Taking $AB = 5.5\ cm, BC = 3.5\ cm$ and $\angle B = 75^\circ ,$ construct $\triangle ABC.$
$2)$Now, construct $\triangle ADC.$
$3)\text{ ABCD}$ is the required parallelogram.

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Question 24 Marks

Construct a regular hexagon of side $3.5\ cm$

Answer

Steps of Construction:
$1)$ Draw a circle with radius $= 3.5\ cm.$
$2)$ Take a point $A$ on the circle. With A as centre and radius is $3.5\ cm$ cut the circle at $B$ and from $B$ with radius $3.5\ cm$ cut the circle at $C$ and so on.
$3)$ Join $AB, BC, CD, DE, EF, AF$
$4) \text{ABCDEF}$ is the required regular hexagon.

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Question 34 Marks

Construct a rectangle $\text{ABCD}$ with one diagonal $AC = 5.8\ cm$ and the acute angle between the diagonals is equal to $45^\circ .$

Answer

Steps of Construction:
$1)$ Draw $A C=5.8 \ cm$ and locate its mid$-$point $O$.
$2)$ Draw line $\text{BOD}$ such that $\angle DOC =45^{\circ}$ and $OB = OD =\frac{1}{2} BD =\frac{1}{2} \times 5.8 \ cm =2.9 \ cm$.
$3)$ Join $A B, B C, C D$ and $D A$.
$4)\text{ABCD}$ is the required rectangle.

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Question 44 Marks

Construct a rectangle $\text{ABCD}$, when $AB = 5\ cm$ and $BC = 6.2\ cm.$

Answer

Steps of construction:
$1$. Draw $B C=6.2 \ cm$
$2$. Through $B$, draw $B P$ such that $\angle B=90^{\circ}$
$3$. From $B P$, cut $B A=5 \ cm$
$4$. With $A$ and $C$ as centres and radii $6.2 \ cm$ and $5 \ cm$ respectively, draw arcs cutting each other at $D$.
$5$. Join $A D$ and $C D$.
Thus, $\text{ABCD}$ is the required triangle.

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MATHEMATICS [4 marks sum]

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