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 3 and quadrilateral 4
quadrilateral 1 and quadrilateral 4
quadrilateral 2 and quadrilateral 3

Answer 1

Answers:
True
Not True
Not True
True

Answer 2

Answer:- 1. Congruent .

2. Not Congruent .

3. Not Congruent .

4. Not Congruent .

Explanation:-

A basic rigid transformation is a transformation of the figure that does not affect the size of the figure . The size of figure doesn't reduce or get enlarge. There are three basic rigid transformations:-reflections, rotations, and translations.

1. Reflection:- A reflection is a transformation that maps every point of a figure in the plane to point of image of figure, across a line of reflection .

2.Rotation:-A rotation of some degrees is a transformation which rotate a figure about a fixed point called the center of rotation.

3.Translation:-A translation is a transformation of a figure that moves every point of the figure a fixed distance in a particular direction.

Now,

1. Quadrilateral 1 and quadrilateral 2 are congruent by reflection.

2. Quadrilateral 3 and quadrilateral 4 are not congruent by using any rigid transformation.

3.Quadrilateral 1 and quadrilateral 4 are not congruent by using any rigid transformation.(as 4 is not a reflected image of 1)

4.Quadrilateral 2 and quadrilateral 3 are not congruent by using any rigid transformation.