Question

When a diagonal is drawn in a rectangle, what is true of the areas of the two triangles into which it divides the rectangle?

One is double the other
They are equal
There is no specific relationship.

Answer 1

The 2 triangles are equal in area

Answer 2

The have the same area.

Explanation:

In the attached figure there is a rectangle ABCD with one diagonal drawn, AC. Now we are going to prove that the triangles ABC and ADC are equal, because, if they are equal they must have the same area.

Notice that:

• the segments AB and DC have the same length, because they are opposite sides of a rectangle,
• the segments CB and DA have the same length because they are opposite sides of a rectangle,
• the segment AC is a common side to both triangles.

Hence, the triangles ABC and ADC have their three side of the same length. Therefore, the triangles ABC and ADC are equals.