Question
Construct a triangle using the given data: $PQ = 6.2\ cm, QR = 9.0\ cm$ and $\angle Q = 30^\circ $
✓
Answer
$PQ = 6.2\ cm, QR = 9.0\ cm$ and $\angle Q = 30^\circ $
Steps of Construction:
$1$. Draw a line segment $PQ = 6.2\ cm$
$2.$ With $Q$ as centre, draw an arc cutting $PQ$ at $M.$
$3$. With $M$ as centre and same radius, cut the arc at $N$. Join $QN.$
$4$. Bisect $\angle NQP$. Let $QY$ be the bisector. $QY$ makes an angle of $30^\circ $ with $PQ.$
$5$. With $Q$ as centre and radius $9\ cm$ cut an arc on $QY$. Mark the point as $R.$
$6$. Join $PR.$
Thus, $\text{PQR}$ is the required triangle.
Steps of Construction:
$1$. Draw a line segment $PQ = 6.2\ cm$
$2.$ With $Q$ as centre, draw an arc cutting $PQ$ at $M.$
$3$. With $M$ as centre and same radius, cut the arc at $N$. Join $QN.$
$4$. Bisect $\angle NQP$. Let $QY$ be the bisector. $QY$ makes an angle of $30^\circ $ with $PQ.$
$5$. With $Q$ as centre and radius $9\ cm$ cut an arc on $QY$. Mark the point as $R.$
$6$. Join $PR.$
Thus, $\text{PQR}$ is the required triangle.
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Case Study : Ankita took part in a Rangoli Competition. She made a beautiful Rangoli in the shape of a triangle ABC as shown. In the triangle, $P, Q$ and $R$ are mid-points of the sides $A B, B C$ and $C A$ respectively. She decorated it by putting a garland along the sides of $\triangle PQR$. The lengths of the sides of the triangle are $AB =20 cm, BC$ $=26 cm$ and $AC =24 cm$.
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