3.11 Quiz: Congruence and Rigid Motions

The rule (x,y)→(−x,−y) maps △RST to △R′S′T′. Which statement correctly describes the relationship between △RST and △R′S′T′?

The triangles are congruent because △R′S′T′ is a rotation of△RST , and a rotation is a rigid motion.

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

△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 △JKL and △J′K′L′? https://static.k12.com/nextgen_media/assets/8080637-NG_GMT_E_01_U03_Quiz_02.png Paste and copy the link above to see the picture

△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(−3, 4), Q(−3, 1), and R(−1, 1). The coordinates of the vertices of △P′Q′R′ are P′(−6, −5), Q′(−6, −1), and R′(−4, −1). Which statement correctly describes the relationship between △PQR and △P′Q′R′?

△PQR is not congruent to △P′Q′R′ because there is no sequence of rigid motions that maps △PQR to △P′Q′R′.

△RST is mapped to △R′S′T′ using the rule (x, y)→(x, −y) followed by (x, y)→(3x, 3y). Which statement correctly describes the relationship between △RST and △R′S′T′?

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