4.05 Quiz: Triangle Congruence and Rigid Motions

The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′. Which statement correctly describes the relationship between △DEF and △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.

Which statement correctly describes the relationship between △JKL and △J′K′L′?

△JKL is not congruent to △J′K′L′ because there is no sequence of rigid motions that maps △JKL to △J′K′L′.

The coordinates of the vertices of △PQR are P(1, 4), Q(2, 2), and R(−2, 1). The coordinates of the vertices of △P′Q′R′ are P′(−1, 4), Q′(−2, 2), and R′(2, 1).

△PQR is congruent to △P′Q′R′ because you can map △PQR to △P′Q′R′ using a reflection across the y-axis, which is a rigid motion.

△RST is mapped to △R′S′T′ using the rule (x, y)→(x, −y) followed by (x, y)→(3x, 3y).

△RST is not congruent to △R′S′T′ because the rules do not represent a sequence of rigid motions.