Geometry

Hong Kong

Stage 1 - Stage 3

Lesson

Lets have a look at the triangle image above.

What relationships do we know exist?

We know that $y+z=180$`y`+`z`=180, because Adjacent angles on a straight line are supplementary (they add up to $180$180 degrees).

We also know that $w+x+y=180$`w`+`x`+`y`=180 because The angle sum of a triangle is $180$180 degrees.

Since both of these equations sum to $180$180, we know that they are both equal. This means that we have

$y+z=w+x+y$`y`+`z`=`w`+`x`+`y`.

Subtracting $y$`y` from both sides of the equation gives us the result

$z=w+x$`z`=`w`+`x`.

Have a look at where these angles are positioned on the triangle.

This special relationship is used frequently in solving geometrical problems. We say formally that the: exterior angle of a triangle is equal to the sum of the two opposite interior angles. Can you see how this statement is a descr