Question

If scalene triangle MNP is rotated to form triangle TUV, which statement must be true?

1) The angles of triangle MNP are equal to the angles of triangle TUV.
2) The sides of triangle MNP are equal to the sides of triangle TUV.
3) The area of triangle MNP is equal to the area of triangle TUV.
4) The perimeter of triangle MNP is equal to the perimeter of triangle TUV.

Answer 1

In a rotation of a triangle, the angles remain the same, but the sides, area, and perimeter generally change.

Step-by-step explanation:

In a rotation, the angles of a triangle do not change. So, the first statement, 'The angles of triangle MNP are equal to the angles of triangle TUV,' must be true. However, the sides of the triangle will generally change. Therefore, the second statement, 'The sides of triangle MNP are equal to the sides of triangle TUV,' is not necessarily true. The area of the triangle will also change, so the third statement, 'The area of triangle MNP is equal to the area of triangle TUV,' is also not necessarily true. Finally, the perimeter of the triangle will generally change, so the fourth statement, 'The perimeter of triangle MNP is equal to the perimeter of triangle TUV,' is not necessarily true either.