Question

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

Answer 1

Answer:

1 and 2 are not congruent; 1 and 3 are congruent; 1 and 4 are congruent; 2 and 3 are not congruent; 2 and 4 are not congruent; 3 and 4 are congruent.

Step-by-step explanation:

From the diagram, we can see that the angle measures and side measures of figures 1, 3 and 4 are the same.  This means that these three figures are congruent.  Figure 2, however, is not congruent to any of the other 3.

Answer 2

Answer:

quadrilateral 1 and quadrilateral 2 NOT CONGRUENT

quadrilateral 1 and quadrilateral 3 CONGRUENT

quadrilateral 1 and quadrilateral 4 CONGRUENT

quadrilateral 2 and quadrilateral 3 NOT CONGRUENT

quadrilateral 2 and quadrilateral 4 NOT CONGRUENT

quadrilateral 3 and quadrilateral 4 CONGRUENT

Step-by-step explanation:

quadrilateral 1 and quadrilateral 2 NOT CONGRUENT

quadrilateral 1 and quadrilateral 3 CONGRUENT:

rigid motion: reflection

axis of reflection: y=x

quadrilateral 1 and quadrilateral 4 CONGRUENT:

rigid motions: translation and reflection

axis of reflection y=0

quadrilateral 2 and quadrilateral 3 NOT CONGRUENT

quadrilateral 2 and quadrilateral 4 NOT CONGRUENT

quadrilateral 3 and quadrilateral 4 CONGRUENT:

rigid motions: translation and reflection

axis of reflection: x=0