Question

The triangles are congruent by the SSS congruence theorem. Which rigid transformation(s) can map ABC onto DEC? reflection, then rotation reflection, then translation rotation, then translation rotation, then dilation

Answer 1

The correct rigid transformations to map congruent triangle ABC onto triangle DEC are a reflection followed by a rotation or a reflection followed by a translation; dilation is not required as congruent triangles are the same size.

Step-by-step explanation:

Given that triangles ABC and DEC are congruent by the Side-Side-Side (SSS) congruence theorem, there are several rigid transformations that can be used to map triangle ABC onto DEC. A rigid transformation is a transformation of a geometric figure that preserves distances and angles. The options include combining reflection, rotation, translation, or dilation. However, considering the congruence, the correct sequence would be a reflection followed by a rotation or a reflection followed by a translation. Dilation would not be needed since congruent triangles are equal in size, and a dilation would change the size of the triangle.

Rotation is defined by the transformation equations x' = x cos Ø + y sin Ø for the x-coordinate, and y' = -x sin Ø + y cos Ø for the y-coordinate. This transformation maintains the distances between points, therefore keeping congruence intact.

Answer 2

reflection, then rotation