geometry - Why does the Angle-Side-Side(Donkey Theroem) not work when finding congruent triangles?

Why does the Angle-Side-Side(Donkey Theroem) not work when finding congruent triangles?

31 viewed last edited 5 years ago

geometry

Anonymous

My teacher explained to me not to use this theorem and not to get it mixed up with the Angle Side Angle theorem, but they never explained what was wrong with it. Could you provide some examples of the Angle-Side-Side theorem not working properly?

Karthikeyan Madathil (last edited 5 years ago) (Expert, Director @ATONARP, Inc.)

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:

http://www.mathwarehouse.com/animated-gifs/images/why-ssa-does-NOT-prove-triangles-congruent-animation.gif

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

http://www.mathwarehouse.com/geometry/congruent_triangles/angle-side-side-postulate.php

Vivekanand Vellanki (last edited 5 years ago) (Expert, Founder @Qalaxia)

Take a look at https://www.qalaxia.com/#/viewDiscussion?messageId=59a51dfb7f173b981abee4a7

The important word in the SAS (side-angle-side) theorem is that the angle is the one subtended between the two sides - this is the angle between the two sides that are equal.