Which statement best explains whether △PQR is congruent to △XYZ?

△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a rotation of 180° about the origin.

△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a translation 5 units down followed by a reflection across the y-axis.

△PQR is not congruent to △XYZ because there is no sequence of rigid motions that maps △PQR to △XYZ.

△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a reflection across the y-axis followed by a reflection across the x-axis.

Question

Eva Boyle

Mathematics

9 November, 04:07

Which statement best explains whether △PQR is congruent to △XYZ?

△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a rotation of 180° about the origin.

△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a translation 5 units down followed by a reflection across the y-axis.

△PQR is not congruent to △XYZ because there is no sequence of rigid motions that maps △PQR to △XYZ.

△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a reflection across the y-axis followed by a reflection across the x-axis.

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Answers (1)

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Marisa Shannon · Answer 1

Two geometic shapes are congruent if one can be mapped to the other only by using rigid motions: translations and rigid rotations. The third statement is the only one that is true for any triangles â-łPQR and â-łXYZ, in whichever position they are.