In various competitions, there are questions related to the Triangle. I have summarized some of the important rules are :
1. The sum of angles of a triangle is 180 degrees.
x +y + z = 180
2. In an isosceles triangle, the altitude from the vertex bisects the base.
Altitude AD from vertex A divides BC into two equal parts:
3. The median* of a triangle divides the triangle into two triangles of the same area.
area of triangle ABD = area of triangle ADC
- Median is the line joining the mid-point a side of a triangle to the opposite vertex.
4. The area of the triangle formed by joining the mid-points of the sides of a given triangle is one-fourth of the area of the given triangle.
AF = FB
BD = DC
are of triangle DEF = 1/4 * area of triangle ABC
5. The centroid* divides each of the medians in the ration of 2:1
- A centroid is a point whee the three medians of a triangle meet.
6. Area of a triangle = 1/2 * base * height
7. Area of a triangle when all sides are known = s(s-a)(s-b)(s-c)
where, s (semi-perimeter) = (a+b+c)/2
This is also called Heron’s formula.