Constructing a Triangle - SAS #3
Triangle from Side-Angle?

A triangle is completely determined if we know 2 "sides" and the size of the angle between them. We have seen this in the previous exercises. What happens if we only know 1 side and 1 angle?

First - click on Goal button to see our goal (hang-on a bit, sometimes it takes it a few seconds).

       

(1) Click and drag the blue points A or B of the triangle. Note that the triangle is always a congruent triangle since the sides and angle do not change (don't move the sliders - that does change the side and angle :) .

(2) Now click and drag the point D - the whole triangle changes. This is because the length of side AD is NOT fixed as it was in all of the previous exercises! So many, many - that is infinitely many - triangles exist when we only fix 1 side and 1 angle.

(3) Finally click on Reset to start.

       

Start: Construct a triangle with a side of length "a" and angle "α" - We start as before, that is:

-Segment-Length Select the 'Segment with given length from point' tool. Click once in the bottom left of the drawing pad to get point A and then enter "a" (no quotes) for the length. We now have Side AB.

-Angle-Size Select the 'Angle of given size' tool. Click on the points B and then A. Erase the entry and select α from the right drop-down menu. An angle marker and point C will appear.

-Line-2pt Select the 'Line through two points" tool. Click on A and then on C. We now have Angle α. Note that C is NOT a point on our triangle!

Now here we stop following our old directions since we do NOT have a fixed length for this side. So we can pick any point on the line AC.

-Point Select the 'Point' tool. Click anywhere on the line AC (above A so the angle is correct). Notice that this point is blue. That means it is a free object - not totally free, but it can be moved anywhere along the line AC. That is, the third point of our triangle is not fixed!

Hide the line AC, hide the point C. (Right-click and deslect 'Show object'.)

-segment Select the 'Segment between two points' tool and draw A and D and then on D and B to complete the triangle.

End: The difference between SAS (side-angle-side) and SA is that the third point of the triangle is not defined completely - we only know that it is on the line AC but not where on the line. For that we need the length of the second side, i.e. the second S in SAS!

        

 

Author: LFS, Created with GeoGebra

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