Question

Triangle LMN is transformed by using a combination of 3 different transformations. Which combination of transformations would result in a triangle that is congruent to Triangle LMN?

Answer 1

A combination of translation, reflection, and rotation applied to Triangle LMN results in a triangle congruent to the original, as these transformations do not change the size or shape of the triangle.

Step-by-step explanation:

To find a combination of transformations that would produce a triangle congruent to Triangle LMN, we must look for transformations that preserve size and shape. These transformations are known as 'rigid motions' or 'isometries'. The three types of rigid motions that will result in a congruent triangle are:

• Translation: Moves every point of the shape the same distance in the same direction.
• Reflection: Flips the shape over a line, creating a mirror image.
• Rotation: Turns the shape around a fixed point.

When we apply any combination of these three transformations—translation, reflection, and rotation—to Triangle LMN, the resulting triangle will be congruent to the original. It is important to note that the congruent triangles will have equal corresponding sides and angles as Triangle LMN.