Draw: Bisectors, Altitudes and Medians

Draw the Angle Bisector of a Given Triangle

Draw bisectors of angle of $\triangle ABC$.

Given: $ABC$ is a triangle and $\angle A$, $\angle B$ and $\angle C$ are its angles.

Required: To draw bisectors of $\angle A$, $\angle B$ and $\angle C$.

Construction:

1. Draw the triangle $ABC$.

   

2. With point $B$ as a centre draw an arc of any radius, intersecting the sides $\overline{BC}$ and $\overline{BA}$ at points $L$ and $M$.

   

3. Take point $L$ as a centre and draw an arc of any radius.

   

4. Now take point $M$ as centre and with the same radius draw another arc, which cuts the previous arc at point $P$.

   

5. Join point $P$ to $B$ and produce it. $BP$ is the bisector of $\angle B$.

   

6. Repeat above steps to draw the bisectors of remaining angles.

Draw the Perpendicular Bisector of a Given Triangle

Draw perpendicular bisectors of sides of $\triangle ABC$.

Given: ABC is a triangle and $\angle A$, $\angle B$ and $\angle C$ are its angles.

Required: To draw perpendicular bisectors of $\overline {AB}$, $\overline {BC}$ and $\overline {AC}$.

Construction:

1. Draw the triangle ABC.

   

2. To draw perpendicular bisectors of side $\overline{AB}$, check if the compass radius is greater than half the length of side $\overline{AB}$. Place the pointed end of the compass at point B and draw two arcs on either side of $\overline{AB}$.

   

3. Without changing the compass radius, place the pointed end at point A and draw two additional arcs on either sides, cutting previous arcs at P and Q.

   

4. Join points P and Q to form the angle bisector line PQ, which bisects side $\overline{AB}$ perpendicularly.

   

5. Next, repeat above steps to construct the perpendicular bisectors of sides BC and AC.

   

6. Hence, $\overline{PQ}$, $\overline{ST}$ and $\overline{LM}$ are the required perpendicular bisectors of the sides $\overline{AB}$, $\overline{BC}$ and $\overline{AC}$ of the given triangle.

   

Draw Altitudes of a Given Triangle

Draw altitudes of $\triangle ABC$.

Given: $ABC$ is a triangle and $\angle A$, $\angle B$ and $\angle C$ are its angles.

Required: To draw altitudes of $<strong><em>\triangle ABC$.

Construction:

1. Draw the triangle $ABC$.

   

2. Take point A as centre and draw an arc of suitable radius, which cuts $\overline{BC}$ at points $D$ and $E$.

   

3. From $D$ as centre, draw an arc of radius more than $\frac12 m \overline DE$.

   

4. Again from point $E$ draw another arc of same radius, cutting first arc at point $F$.

   

5. Join the points $A$ and $F$. Such that AF intersects $\overline {BC}$ at point P. Then $\overline {AP}$ is the altitude of the $<strong><em>\triangle ABC$ from the vertex $A$.

   

6. Repeat above steps to draw altitudes from vertices $B$ and $C$.

   

7. Hence, $\overline {AP}$, $\overline {BQ}$ and $\overline {CR}$ are the altitudes of given triangle.

   

Draw Medians of a Given Triangle

Draw medians of $\triangle ABC$.

Given: $ABC$ is a triangle.

Required: To draw medians of $\triangle ABC$.

Construction:

1. Draw the triangle $ABC$.

   

2. Bisect the sides $\overline {AB}$, $\overline {BC}$ and $\overline {AC}$ at points $D, E$ and $F$ respectively.

   

3. Join $A$ to $E, B$ to $F$ and $C$ to $D$.

   

4. Thus $\overline {AE}$, $\overline {BF}$and $\overline {CD}$ are the required medians of the $\triangle ABC$.