Karthikeyan Madathil

Take an Angle T and the two sides S1 and S2

Draw a straight line on paper. Now draw another line that makes an angle T with it using your protractor. Call the point of intersection between the two lines A. Adjust your compass to length S1, and draw an arc with centre A intersecting your second line. Call the point where it intersects the line B. Now, adjust your compass to length S2, and draw a circle with centre at B. You will notice that it intersects the first line at two points, call them C and D.

Now, both triangles ABC and ABD meet your original specification (T, S1, S2). However, they are clearly not congruent.

For a visual demonstration of this idea, please see the following picture:


You can see their explanation at (using different, but equivalent language):