Question

Which pairs of quadrilaterals can be shown to be congruent using rigid motions?



Select Congruent or Not congruent for each pair of quadrilaterals.

Congruent Not congruent
quadrilateral 1 and quadrilateral 2


quadrilateral 2 and quadrilateral 3


quadrilateral 1 and quadrilateral 4


quadrilateral 3 and quadrilateral 4


Four quadrilaterals on a coordinate plane. Quadrilateral 1 has vertices at 2 comma 1, 2 comma 5, 6 comma 4, and 7 comma 1. Quadrilateral 2 has vertices at negative 2 comma 2, negative 2 comma 6, negative 6 comma 5, negative 7 comma 2. Quadrilateral 3 has vertices at negative 3 comma negative 2, negative 2 comma negative 5, negative 7 comma negative 5, and negative 7 comma negative 2. Quadrilateral 4 has vertices at 1 comma negative 2, 5 comma negative 2, 4 comma negative 6, and 1 comma negative 7.

Answer 1

Answers:

- Quadrilateral 1 and Quadrilateral 2: Congruent.
- Reason: Side lengths (in order) are 4, √17, √10, 5 for both shapes, so one is a reflection/translation of the other.

- Quadrilateral 2 and Quadrilateral 3: Not congruent.
- Reason: Q2 side lengths are 4, √17, √10, 5 while Q3 has side lengths √10, 5, 3, 4 (one side = 3), so they cannot match by a rigid motion.

- Quadrilateral 1 and Quadrilateral 4: Congruent.
- Reason: Q4 also has side lengths 4, √17, √10, 5 (same sequence as Q1), so Q4 is a rigid-motion image of Q1.

- Quadrilateral 3 and Quadrilateral 4: Not congruent.
- Reason: Q3 has a side of length 3 while Q4 does not, so no rigid motion can make them coincide.