Question

Triangle ABC is graphed in Quadrant I of a coordinate plane, and none of the vertices have an x-coordinate or

y-coordinate of 0. Triangle ABC is rotated 90° clockwise with the origin as the center of rotation to create triangle
A'B'C'.
Which statement must be true?
А)
The sum of the angle measures of triangle A'B'C' is 90° more than the sum of the angle measures of
triangle ABC
B The side lengths of triangle A'B'C' are greater than their corresponding side lengths of triangle ABC.
Each angle measure of triangle ABC is less than the corresponding angle measure of triangle A'B'C'.
D. The corresponding sides of triangle ABC and triangle A'B'C' are congruent.

Answer 1

Explanation:

D. the corresponding sides of triangle ABC and triangle A'B'C' are congruent

because the sides do not change their length when we rotate the triangle

Answer 2

A rotation of 90° does not change the sum of angle measures or the side lengths of a triangle. Therefore, statement D is correct; the corresponding sides of triangle ABC and triangle A'B'C' are congruent.

The question asks for the properties of a triangle that has been rotated 90° clockwise around the origin, specifically comparing the result to the original triangle. Given that a rotation in geometry is a transformation that turns a figure about a fixed point called the center of rotation without changing its size or shape, we know the following:

The sum of the angle measures of any triangle is always 180°, irrespective of any rotation.

The side lengths of a triangle remain unchanged through a rotation, meaning that corresponding sides of the original and rotated triangles are congruent.

The angle measures stay the same because rotation is a rigid motion, hence each angle measure of triangle ABC is equal to the corresponding angle measure of triangle A'B'C'.

Therefore, the correct statement is that the corresponding sides of triangle ABC and triangle A'B'C' are congruent (D).