A series of transformations on triangle S resulted in triangle T.

Question

• The angle measures of triangle T are congruent to those of triangle S.

• The side lengths of triangle T are twice as long as those of triangle S.

Which transformation on triangle S must be included to result in triangle T?
Responses
A RotationRotation
B ReflectionReflection
C DilationDilation
D Translation

Answer 1

To determine the transformation that resulted in triangle T from triangle S, we can analyze the properties of the triangles described:

1. The angle measures of triangle T are congruent to those of triangle S. This indicates that the shapes of both triangles are similar.

2. The side lengths of triangle T are twice as long as those of triangle S. This indicates a change in size while maintaining the same shape.

When considering the options:

• A. Rotation: This transformation would change the orientation but not the size of the triangle.

• B. Reflection: Similar to rotation, this alters the orientation without affecting size.

• C. Dilation: This transformation preserves the shape (congruent angles) while changing the size proportionally. Since the side lengths of triangle T are twice those of triangle S, this could be a dilation with a scale factor of 2.

• D. Translation: This moves the triangle without changing its shape or size.

Given that triangle T has the same angles as triangle S and its sides are doubled in length, the transformation that must be included is Dilation.

Therefore, the correct answer is C. Dilation.