3.12 Congruence and Rigid Motions

The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′.

The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.

The coordinates of the vertices of △ABC are A(−1, 1), B(−2, 3), and C(−5, 1). The coordinates of the vertices of △A′B′C′ are A′(−1, −4), B′(−2, −6), and C′(−5, −4).

△ABC is congruent to △A′B′C′ because you can map △ABC to △A′B′C′ using a reflection across the x-axis followed by a translation 3 units down, which is a sequence of rigid motions.

The coordinates of the vertices of △ABC are A(1, 1), B(5, 1), and C(5, 3). The coordinates of the vertices of △A′B′C′ are A′(−1, −1), B′(−5, −1), and C′(−5, −3).

△ABC is congruent to △A′B′C′ because you can map △ABC to △A′B′C′ using a rotation of 180° about the origin, which is a rigid motion.

Which statement correctly describes the relationship between △ABC and △A′B′C′?

△ABC is congruent to △A′B′C′ because you can map △ABC to △A′B′C′ using a translation 6 units to the left, which is a rigid motion.

△DEF is mapped to △D′E′F′ using the rule (x, y)→(x, y+1) followed by (x, y)→(x, −y).

△DEF is congruent to △D′E′F′ because the rules represent a translation followed by a reflection, which is a sequence of rigid motions.