While solving different questions , I realized that whenever I constructed an altitude it always bisected the base in half. From what I deduced from Wikipedia is that this is only true if the triangle is either isosceles or a right triangle. What I really want to know is when I am given a question sometimes the type of triangle is not specified however I am still required to draw altitudes and assume they cut the emerging angle in half and also cut the other side in half. As shown in the following figures in red.Is there any safe way to make sure that the altitude i am drawing will definitely cut the base in half ? or do I have to first make a wise estimate of the type of triangle before constructing an altitude.
Best Answer
Firstly, your statement : "whenever I constructed an altitude it always bisected the base in half. From what I deduced from Wikipedia is that this is only true if the triangle is either isosceles or a right triangle" is not fully correct. An altitude from a vertex bisects the opposite base if and only if the two sides emerging from that particular vertex are equal(not necessary in a right angle triangle).Therefore, you need to specify this condition before assuming that the altitude cuts the opposite base in half.