Question

Draw a triangle $ABC$. Draw a median $BE$ altitude $BD$ in it.

Answer 1

Steps of construction:

Draw a rough diagram for triangle $ABC$.

(i) To draw the Altitude from vertex $B$,

1. Extend the line from the points $A,C$ respectively.

2. Draw the arc from the centre $B$, such that, arc cuts the line $AC$ at $P$ and $Q$ respectively.

3. With $P$ and $Q$ as centres and more than half the distance between these as radius draw two arcs to intersect each other at $R$.

4. Join $BR$, which intersects $AC$ at the point $D$.

Clearly, $BD\perp AC$,

Hence, altitude $BD$ is formed.

(ii) To draw the Median from vertex $B$.

1. Draw the arcs on both sides of the side $AC$ with the radius is more than $\frac{1}{2}AC$ from the centres $A,C$. these arcs are intersected at $S,T$ respectively.

2. Join $ST$, which intersect $AC$ at the point $E$, such that $AE=CE$.

i.e, $E$ is the mid-point of the side $AC$.

3. Join $BE$.

Hence, median $BE$ is formed.