Question

Triangle MNO is transformed to produce Triangle PQR. Select all of the transformations that would guarantee that triangles MNO and PQR are congruent.

a. A dilation, then a translation
b. A reflection, then a rotation
c. A rotation, then a dilation
d. A translation, then a rotation
d. A reflection, then a translation

Answer 1

Triangles MNO and PQR will be congruent if the transformation is a reflection followed by a rotation, a rotation followed by a reflection, a translation followed by a rotation, or a reflection followed by a translation, as these transformations maintain the size and shape of the triangle.

Step-by-step explanation:

The question asks about the transformations that would guarantee Triangle MNO and Triangle PQR are congruent. Congruency of triangles is maintained through transformations that do not affect the size and shape of the triangle, such as translations, rotations, and reflections. However, dilation changes the size of the triangle, and hence, options including dilation will not result in congruent triangles.

The correct transformations are:

• Reflection, then a rotation
• Rotation, then a reflection
• Translation, then a rotation
• Reflection, then a translation

These transformations do not alter the dimensions or the angles of the triangles, which is why the triangles MNO and PQR will remain congruent after any combination of these transformations.