Question

which statement explains why the triangles are congruent?
o you can map one triangle onto the other by performing a 180° rotation about the origin, and a rotation is a rigid transformation.
o you can map one triangle onto the other by performing a 90° rotation about the origin, and a rotation is a rigid transformation.
o you can map one triangle onto the other by performing a reflection across the y - axis, and a reflection is a rigid transformation.
o you can map one triangle onto the other by performing a translation, and a translation is a rigid transformation.

Explanation:

Step1: Analyze the orientation of triangles

By observing the graph, we can see that the two triangles are mirror - images of each other with respect to the y - axis.

Step2: Recall rigid - transformation rules

Rigid transformations (rotation, reflection, translation) preserve the shape and size of a figure. A reflection across the y - axis changes the sign of the x - coordinates of the vertices of a figure while keeping the y - coordinates the same.

Step3: Evaluate each option

180° and 90° rotations about the origin would change the orientation in a different way than what is shown. A translation would just move the triangle without flipping it. A reflection across the y - axis can map one triangle onto the other.

Answer:

You can map one triangle onto the other by performing a reflection across the y - axis, and a reflection is a rigid transformation.