Question

side - angle - side (sas)
move points f until you have a triangle. you can also move points a, b, or c from the first triangle to change the size.
can you make a triangle that is a different size or shape than △abc? why or why not?

Explanation:

Step1: Recall SAS congruence criterion

The Side - Angle - Side (SAS) congruence criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the two triangles are congruent.

Step2: Analyze given triangles

In \(\triangle ABC\) and \(\triangle DEF\), we have two sides and the included angle equal. So, by SAS, any triangle constructed with the same two - side lengths and the same included - angle measure will be congruent to \(\triangle ABC\).

Answer:

No, you cannot make a triangle that is a different size or shape than \(\triangle ABC\) because of the Side - Angle - Side (SAS) congruence criterion. When two sides and the included angle of one triangle are fixed (as in the given setup), the shape and size of the triangle are uniquely determined.