[3 marks sum]

Question 13 Marks

Construct an equilateral triangle using the given data: Altitude $OM = 5.8 \ cm$

Answer

Altitude $OM = 5.8 \ cm$

Steps of construction:
$1.$ Draw a line segment $ST$ of any length.
$2.$ Through a point $M$ on $ST,$ draw $PM$ perpendicular to $ST$ such that $OM = 5.8 \ cm.$
$3.$ Through $O,$ draw $OQ $and $OR$ making angles equal to $30^\circ $ with $OM$and meeting $ST$ at $Q$ and $R$ respectively.
Thus, $\text{OQR}$ is the required triangle.

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Question 23 Marks

Construct an equilateral triangle using the given data: Altitude $PM = 3.6 \ cm$

Answer

Altitude $PM = 3.6 \ cm$

Steps of construction:
$1.$ Draw a line segment $ST$ of any length.
$2. $Through a point $M$ on $ST,$ draw $PM$ perpendicular to $ST$ such that $PM = 3.6 \ cm.$
$3.$ Through $P,$ draw $PQ$ and $PR$ making angles equal to $30^\circ $ with $PM$ and meeting $ST$ at $Q$ and $R$ respectively.
Thus, $\text{PQR}$ is the required triangle.

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Question 33 Marks

Construct an equilateral triangle using the given data: Altitude $AD = 5 \ cm$

Answer

Altitude $AD = 5 \ cm$

Steps of construction:
$1.$ Draw a line segment $PQ$ of any length.
$2.$ Through a point $D$ on $PQ,$ draw $AD$ perpendicular to $PQ$ such that $AD = 5 \ cm.$
$3.$ Through $A,$ draw $AB$ and $AC$ making angles equal to $30^\circ $ with $AD$ and meeting $PQ$ at $B$ and $C$ respectively.
Thus, $\text{ABC}$ is the required triangle.

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Question 43 Marks

Construct an isosceles triangle in which$:$ Base $QR = 5.2 \ cm$ and the altitude $PM = 4.8 \ cm$

Answer

Steps:
$1.$ Draw $QR = 5.2\ cm.$
$2.$ Draw $AMB,$ a perpendicular bisector of $QR.$
$3.$ With $M$ as centre and radius $4.8\ cm,$ draw an arc to cut $MN$ at $P.$
$4.$ Join $PQ$ and $PR.$
Thus$, \text{PQR}$ is required triangle.

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MATHEMATICS [3 marks sum]

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