Question
Construct a triangle using the given data: $XY = 5.2\ cm, XZ = 6.5\ cm$ and $\angle X = 75^\circ $
✓
Answer
$XY = 5.2\ cm, XZ = 6.5\ cm$ and $\angle X = 75^\circ $
Steps of Construction:
$1.$ Draw a line segment $XY = 5.2\ cm.$
$2.$ With $X$ as centre, draw an arc cutting $XY$ at $L.$
$3.$ With $L$ as centre and the same radius, cut the arc at $M$ and then from $M$, with same radius, cut the arc at $N$.
$4$. With $M$ and $N$ as centre bisect $\angle MXN$ thus formed to draw a ray $XP.$
$5$. Again bisect the $\angle MXP$. Let $XR$ be the bisector.$XR$ makes an angle of $75^\circ $ with $XY.$
$6$. With $X$ as centre and radius $6.5\ cm$ cut an arc on $XR$ and mark the point as $Z.$
$7$. Join $YZ.$
Thus, $\text{XYZ}$ is the required triangle.
Steps of Construction:
$1.$ Draw a line segment $XY = 5.2\ cm.$
$2.$ With $X$ as centre, draw an arc cutting $XY$ at $L.$
$3.$ With $L$ as centre and the same radius, cut the arc at $M$ and then from $M$, with same radius, cut the arc at $N$.
$4$. With $M$ and $N$ as centre bisect $\angle MXN$ thus formed to draw a ray $XP.$
$5$. Again bisect the $\angle MXP$. Let $XR$ be the bisector.$XR$ makes an angle of $75^\circ $ with $XY.$
$6$. With $X$ as centre and radius $6.5\ cm$ cut an arc on $XR$ and mark the point as $Z.$
$7$. Join $YZ.$
Thus, $\text{XYZ}$ is the required triangle.
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