Question

Perform the following straightedge and compass construction. State all steps as clearly as possible
- The Orthocenter of a non regular triangle

Answer 1

Orthocenter is the intersection point of any 2 or 3 altitude(The 3rd median is required for verify the intersection point, It can be avoid for finding orthocenter) .

To construct the orthocenter, Consider triangle ABC

Step 1- Altitude from vertex C to side AB

a) Draw an altitude from vertex C to opposite side AB

b) Point the compass on vertex C, and make 2 arc cut at 2 diffrent points in opposite side AB

c) Now find bisect the line between the intersection point. and join the bisected midpoint to vertex C. We got the altitude from vertex C to side AB. which will be perpandicular to side AB

Step 2- Altitude from vertex B to side AC

a) Draw an altitude from vertex B to opposite side AC

b) Point the compass on vertex B, and make 2 arc cut at 2 diffrent points in opposite side AC

c) Now find bisect the line between the intersection point. and join the bisected midpoint to vertex B. We got the altitude from vertex B to side AC. which will be perpandicular to side AC

The intersection point od Altitudes BF and CF is at O, and point O is known as Orthocenter

Verify the point is same with the third altitude from vertex A to opposite side CB with same procedure. This step is not necessery to find altitude