[4 marks sum]

Question 14 Marks

Construct an isosceles triangle in which: Base $BC = 6.4 \ cm$ and side $AB = 7.2 \ cm$

Answer

In the given isosceles $\triangle ABC,$
Base $BC = 6.4\ cm$, Side $AB = 7.2\ cm$
$\Rightarrow AB = AC = 7.2\ cm$
Steps:
$1$. Draw $BC = 6.4\ cm$
$2$. With $B$ as centre and radius $7.2\ cm$, draw an arc.
$3.$ With $C$ as centre and radius $7.2\ cm$, draw another arc to cut the first arc at $C$.
$4$. Join $AB$ and $AC$
Thus, $\text{ABC}$ is required triangle.

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Question 24 Marks

Construct an isosceles triangle in which: $PQ = QR, PR = 4.5 \ cm$ and $\angle R = 60^\circ $

Answer

In $\triangle PQR,$
$PQ = QR ....($given$)$
$\Rightarrow \angle PRQ = \angle RPQ = 60^\circ $
Steps:
$1$. Draw $PR = 4.5\ cm.$
$2$. Construct $\angle PRU = 60^\circ $ and $\angle RPV = 60$
$3.$ Ray $RU$ and $PV$ meet at $Q$.
Thus, $\text{PQR}$ is the required triangle.

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Question 34 Marks

Construct a right$-$angled triangle in which Side $DE = 6 \ cm$ and $\angle E = 30^\circ , \angle D = 90^\circ $

Answer

Steps:
$1$. Draw $DE = 6\ cm.$
$2$. At $D$, construct $\angle PDE = 90^\circ $
$3$. With $E$ as centre, draw $\angle DEM = 30^\circ $
$4$. Ray $DP$ and ray $EM$ intersect at $F.$
Thus, $\text{DEF}$ is the required triangle.

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Question 44 Marks

Construct a right$-$angled triangle in which: Side$ AB = 4.5 \ cm$ and hypotenuse $AC = 7 \ cm$

Answer

Steps:
$1$. Draw $AB = 4.5\ cm$
$2$. At $B$ construct a ray $BP$ such as $\angle ABP = 90^\circ $
$3$. With $A$ as a centre and radius $7\ cm$, draw an arc to cut $BP$ at $C.$
$4$. Join $AC.$
Thus, $\text{ABC}$ is the required triangle.

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Question 54 Marks

Construct a triangle using the given data: $BC = 6\ cm, AC = 5.0\ cm$ and $\angle C = 60^\circ $

Answer

$BC = 6\ cm, AC = 5.0\ cm$ and $\angle C = 60^\circ $

Steps of Construction:
$1.$ Draw a line segment $BC = 6\ cm.$
$2. $With $C$ as centre, draw an arc to cut $BC$ at $P.$
$3.$ With $P$ as centre and the same radius, cut the arc at $Q.$
$4.$ Draw a ray $CX$ passing $Q. CX$ makes an angle of $60^\circ$ with $BC.$
$5.$ With $C$ as centre and radius $5\ cm$ cut an arc on $CX$ and mark the point as $A.$
$6.$ Join $AB.$
Thus, $\text{ABC}$ is the required triangle.

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Question 64 Marks

Construct a$ \triangle RST$ with side $ST = 5.4 \ cm, \text{RST} = 60^\circ $ and the perpendicular from $R$ on $ST = 3.0 \ cm.$

Answer

Steps of construction:
$1.$ Draw a line segment $ST = 5.4 \ cm.$
$2.$ With S as centre, draw $XS$ making an angle of $60^\circ $ with $S$T i.e. $XST = 60^\circ .$
$3.$ Draw a straight line $PQ$ parallel to $ST$ at a distance of $3 \ cm$ from $ST.$
$4. PQ$ meets $XS$ at $R.$
$5.$ Join $RT.$
Thus, $RST$ is the required triangle with angle $RST = 60^\circ .$

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Question 74 Marks

Construct a triangle using the given data: $DE = 6.5\ cm, EF = 5.8\ cm$ and $DF = 4.2\ cm$

Answer

$DE = 6.5\ cm, EF = 5.8\ cm$ and $DF = 4.2\ cm$

Steps of Construction:
$1.$ Draw $DE = 6.5\ cm$
$2.$ With $D$ as centre and radius $4.2\ cm$, draw an arc.
$3.$ With $E$ as centre and radius $5.8\ cm$, draw another arc to cut the first arc at $F.$
$4.$ Join $DF$ and$ EF.$
Thus, $\text{DEF}$ is the required triangle.

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Question 84 Marks

Construct a triangle using the given data: $PQ = 4.8\ cm, QR = 6.3\ cm$ and $PR = 5.5\ cm$

Answer

$PQ = 4.8\ cm, QR = 6.3\ cm$ and $PR = 5.5\ cm$

Steps of Construction:
$1.$ Draw $PQ = 4.8\ cm$
$2.$ With $P$ as centre and radius $5.5\ cm$, draw an arc.
$3.$ With $Q$ as centre and radius $6.3\ cm$, draw another arc to cut the first arc at $R.$
$4.$ Join $PR$ and $QR.$
Thus, $\text{PQR}$ is the required triangle.

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Question 94 Marks

Construct a triangle using the given data: $AB = 6.5\ cm, BC = 8.4\ cm$ and $AC = 7.2\ cm$

Answer

$AB = 6.5\ cm, BC = 8.4\ cm$ and $AC = 7.2\ cm$

Steps of Construction:
$1.$ Draw $AB = 6.5\ cm$
$2.$ With $A$ as centre and radius $7.2\ cm$, draw an arc.
$3.$ With $B$ as centre and radius $8.4\ cm,$ draw another arc to cut the first arc at $C.$
$4.$ Join $AC$ and $BC.$
Thus, $\text{ABC}$ is the required triangle.

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MATHEMATICS [4 marks sum]

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