Construct a triangle using the given data: PQ - PR = 1.5 cm, QR =… - Vidyadip

Question

Construct a triangle using the given data: $PQ - PR = 1.5 \ cm, QR = 6.0$ and $\angle Q = 45^\circ $

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Answer

$PQ - PR = 1.5 \ cm, QR = 6.0$ and $\angle Q = 45^\circ $

Steps of Construction:
$1$. Draw a line segment $QR = 6 \ cm.$
$2$. With $Q$ as centre, draw $\angle TQR = 45^\circ $
$3$. From $QT$, cut $QS = 1.5 \ cm.$
$4$. Join $S$ and $R$.
$5$. Draw perpendicular bisector of $SR$ which cuts $QT$ at $P.$
$6$. Join $PR.$
Thus, $\text{PQR}$ is the required triangle.

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