Handy Rules of Triangles for Mathematics Competition

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.

AB=BC

Altitude AD from vertex A divides BC into two equal parts:

BD=DC

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

AE =EC

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.

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