Question

all triangle with same base and the third vertex on a line parallel to the base have​

Answer 1

Step-by-step explanation:

The area of each triangle is half of the area of any parallelogram on the same base and between the same parallels. Thus, the area of the two triangles is the same. Let us formalize this as a theorem:

Theorem: Two triangles on the same base and between the same parallels are equal in area.

Also, we have already seen how to calculate the area of any triangle. Consider a triangle. Take side BC to be the base of this triangle. Now, measure the height of this triangle, which will be the distance between BC and the parallel to BC through A:

Triangles - Height and Base

In other words, the height of this triangle will be the length of the perpendicular AD (from A to BC). Thus, the area of this triangle can be written as:

A = ½ × BC × AD

Note that there is nothing special about BC – we can take any other side as the base as well. Let us take AC as the base. In that case, the height of the triangle will be the length of the perpendicular from B to AC:

Triangles - Height perpendicular to base

The area of the triangle can now be written as:

A = ½ × AC × BE