Question

angle - angle - side non - corresponding side (aas - nc)
move points e and 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 with aas - nc? why or why not?

Explanation:

Step1: Recall triangle - congruence criteria

The AAS - NC (Angle - Angle - Side Non - Corresponding Side) is not a valid congruence criterion for triangles. Given two angles and a non - corresponding side, we can construct non - congruent triangles.

Step2: Consider angle - side relationships

We can change the length of the non - corresponding side while keeping the two angles the same. This will result in triangles of different sizes and shapes. For example, if we have two angles $\angle A$ and $\angle B$ and a side $BC$, we can extend or shorten the side opposite one of the given angles (the non - corresponding side) to get a different triangle.

Answer:

Yes, we can make a triangle that is a different size or shape than $\triangle ABC$ with AAS - NC. Because AAS - NC is not a congruence criterion and by changing the length of the non - corresponding side, we can create non - congruent triangles with the same two angles.