Question

Triangle a'b'c' is rotated 180° counterclockwise about the origin to form ∆a"b"c". is ∆abc congruent to ∆a"b"c"? give details to support your answer

Answer 1

Triangle ABC is congruent to triangle A"B"C" after a 180° counterclockwise rotation about the origin, as rotations preserve the size and shape of geometric figures.

Step-by-step explanation:

Yes, ∆ABC is congruent to ∆A"B"C" after a 180° counterclockwise rotation about the origin. A rotation by 180° around the origin is an isometry, which means it preserves the size and shape of figures, thus the side lengths and angles of the triangle will remain unchanged. Since congruent triangles have the same shape and size, but may have a different orientation or position, the rotated triangle ∆A"B"C" would have the same side lengths and angle measures as ∆ABC, making them congruent.