A triangle is completely determined if we know 2 "sides" and the size of the angle between them. On the sliders we are given the lengths of 2 "sides" and an angle. Let's construct the triangle!
First - click on Goal button to see our goal (hang-on a bit, sometimes it takes it a few seconds). Before you click on Reset, 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 sides and angle :) . Now click on Reset to start.
Start: Construct a triangle with sides of length "a" and "b" and angle "α".
- 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.
- 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
- 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!
How do we find the third point D of our triangle? (1) The point D must be on the line through AC and (2) the segment AD must be of length "b" .We draw a circle with center A and radius "b" and look for the intersection of this circle and AC. This gives us the point we need.
- Select the 'Circle with center and radius' tool. Click on A and then enter b for the radius.
- Select the 'Intersect two objects" tool and click on the intercetion of the circle and line AC. We now have Side AD.
- Right-click and deslect 'Show object' on line AC, the circle and on the point C.
- Select the 'Segment between two points' tool and click on A and D and then on D and B to complete the triangle.
Now, notice that the position and length of the side BD is fixed. Also the angles ABD and
ADB are also fixed. There are no extra possibilities.
End: Select the move tool. Click and drag the sliders for the sides and angles. Each time a specific triangle is made.
- Now click on the DIY: Do It Yourself button to do this construction all by yourself!.
Authors: LFS-RF, Created with GeoGebra