Question

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

Answer 1

Hint: To obtain the triangle ABC we will follow a set of steps one by one. One side of the triangle is given so draw it first then from point $B$ form an angle of ${{45}^{\circ }}$ below the line $BC$ and name a point $X$ on that line. Then form a perpendicular line on line $BX$ and one perpendicular line on $BC$ the point at which they intersect mark it as $O$ taking $O$ as point and $OB$ as radius form a circle now taking $B$ as a point and $5cm$ in the protractor form two arc on the circle name it $A,{{A}_{1}}$ join $A,B,C$ and ${{A}_{1}},B,C$to get the required triangle.

Complete step-by-step solution:
The things given to us to construct $\Delta ABC$ are:
$BC=6cm$
$\angle A={{45}^{\circ }}$
Median$AD=5cm$
Now, the first step will be to form a line $BC=6cm$ using a ruler.

Now draw an angle of ${{45}^{\circ }}$ from the point $B$ below the line $BC$ and join the two points to get a line $BX$.

Now draw a perpendicular angle on line $BX$ by using a protractor and get,

Now draw a perpendicular bisector of $BC$ and name the point $F$ where line $BE$ and the perpendicular bisector line meet.

Now, taking $F$ as a point and $FB$ a radius draw a circle

Next we will take a length $5cm$ on a protractor and put the protractor on point $B$ and form two arc on the circle on left and right side of $B$ and name them $A,{{A}_{1}}$ as:

So the triangle obtained is $\Delta ABC$

Note: A triangle is a three sided polygon having three angles, three vertices and three sides. Draw the side given first and then as given in the question draw the angle using the point of the sides with the help of a protractor.