Question

Construct a triangle ABC in which $BC=6cm,\angle A={45}^{\circ }$ and median $AD=5cm$.

Answer 1

Steps of Construction :
1. Draw a line segment $BC=6cm$
2. Make an angle PCB = ${45}^{\circ }$ with the help of a protractor
3. Draw the perpendicular bisector $RQ$ of $AB$
4. Draw $BE\perp BP$ at $B$
Let $RQ$ and $BE$ intersect at $O$
5. Draw the circle with centre O and radius OB
Then any angle in the major segment = $\angle PBC={45}^{\circ }$
6. Let $RQ$ intersect $BC$ to $D$ is the mid-point of $BC$. Taking $D$ as centre and $5cm$ radius draw arcs intersecting the circle in $A,A^{\prime }$.
7. Join $AB,AC$ and $A^{\prime }B,A^{\prime }C$
Then the required triangle is $ABC$ or $A^{\prime }BC$.