3.12 Quiz: Congruence and Rigid Motions

The rule (x,y)→(−x,y) maps △ABC to △A′B′C′. Which statement correctly describes the relationship between △ABC and △A′B′C′ ?

The triangles are congruent because △A′B′C′ is a reflection of △ABC , and a reflection is a rigid motion.

The coordinates of the vertices of △JKL are J(3, 0) , K(1, −2) , and L(6, −2) . The coordinates of the vertices of △J′K′L′ are J′(−3, 1) , K′(−1, 3) , and L′(−6, 3) .

△JKL is congruent to △J′K′L′ because you can map △JKL to △J′K′L′ using a rotation of 180° about the origin followed by a translation 1 unit up, which is a sequence of rigid motions.

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

△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) . 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.