Determine whether side-side-angle (SSA) is a valid means for establishing triangle congruence. In this case, you know the measure of two adjacent sides and the angle opposite to one of them. If it is a valid criterion, explain why. If it is not valid, use GeoGebra to create a counterexample demonstrating that it doesn’t work and give an explanation. (Hint: Try constructing a triangle where the known angle is opposite to the shortest known side.) If you construct a counterexample, take a screenshot of your work, save it, and insert the image in the space below.

Congruence of triangles means that two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

In this case, these triangles can be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with each other.

To illustrate the question, this will be:

Step 1: Draw a line segment AB

Step 2:Draw an acute angle (let's say 45° ) at A as AX

Step 3: From B draw an altitude on AX BY ⊥ AX

Step 4 Using suitable compass width and taking Y as center cut AX on both sides at C and D

Now BC = BD as BY is perpendicular bisector

Now compare ΔABC and ΔABD. Using suitable compass width and taking B as center cut AX at 2 points C & D directly so BC = BD.

This can illustrate that SSA is not a valid means for establishing triangle congruence.

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