Draw the triangle that has angles of 40° and 50°, and an included side of length 5cm. 画出角度为40° 和 50°

Again, we’ll start by constructing the first side of the triangle, which is 5cm long.

And again, we’ll use a protractor to measure an angle of 40° around one of the endpoints, and draw the second side of the triangle. However, we don’t yet know where this side will end.

Instead, let’s pick any point around this line, pretend it’s the third vertex of the triangle and measure an angle of 50°.

As you can see, this doesn’t quite work: the third side does not yet link up with the vertex A. To fix this, we simply have to shift it: we draw a parallel line that goes through A. (You already learned how to construct parallel lines in a previous course.)

Now the two angles at the top are alternate angles, so they must be congruent and both 50°. We can erase the incorrect, first line to get our completed AAS triangle.