Question

angle - angle - angle. move points d, e and f. you can also move points a, b or c from the first triangle to change the size and shape of the triangles. can you make a triangle that is a different size or shape than △abc? why or why not?

Explanation:

Step1: Recall AA - AA similarity criterion

If the three angles of one triangle are equal to the three angles of another triangle, the triangles are similar. Similar triangles have the same shape but can have different sizes.

Step2: Analyze the given situation

Since we only have angle - angle - angle (AAA) information, we can make triangles of different sizes. Changing the lengths of the sides while keeping the angles the same changes the size of the triangle.

Answer:

Yes, you can make a triangle that is a different size than △ABC. This is because when only the angles of a triangle are fixed (AAA), the side - lengths can vary, resulting in similar triangles of different sizes.