Constructing an Altitude of a Triangle

Constructing an Altitude of a Triangle:

I. Constructing an Altitude for an Acute Triangle:

1. Draw an Acute angle Triangle ΔXYZ.
2. Draw a perpendicular from vertex X on the side YZ using a set-square. Name the point where it meets side YZ as R. Seg XR is an altitude on
   side YZ.
   
3. Considering side XZ as a base, draw an altitude YQ on side XZ. seg YQ ⊥ seg XZ.
4. Consider side XY as a base, draw an altitude ZP on seg XY. seg ZP ⊥ seg XY.
   
   seg XR, seg YQ, seg ZP are the altitudes of ΔXYZ.
5. Note that, the three altitudes are concurrent. The point of concurrence is called the orthocentre of the triangle. It is denoted by the letter ‘O’.

II. Constructing an Altitude for an Obtuse Triangle:

1. Draw an obtuse triangle. Label it ΔABC, Extend side `bar(AC)`, beyond point A.
   
2. Construct a perpendicular line to `bar(AC)`, through B.