In triangle ABC, point X is the

Douglas Sierra

How do you know that Triangle ABX is half the area of Triangle ABC? Is it enough to assume that if AC is the base and AX= 1/2 AC?

Jan 13, 2017 • Reply

Sam Kinsman

Hi Douglas,

Let's think about the are of triangle ABC. We can make base of the triangle AC, and the height will be the distance between B and the line AC. So the area of triangle ABC is:

AC * (distance between B and the line AC) / 2

Now let's consider the are of triangle ABX. We can make base of the triangle is AX. This is exactly half of the length of AB. The height of the triangle is the distance between B and the line AC. So the height of this triangle is the same as the height of triangle ABC. So the area of triangle ABX is:

AX * (distance between B and the line AC) / 2

So the only difference between the formula for the area of ABC and the formula for the area of ABX is that for ABC, we are using AC, and for ABX we are using AX. We know that AX is half of AC. Therefore, the area of ABX must be half as large as the area of ABC.

Jan 14, 2017 • Reply