G.CO.A.3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

Example Problems

There is exactly one reflection and no rotation that sends the convex quadrilateral

ABCD

onto itself. What shape(s) could quadrilateral

ABCD

be? Explain.

Suppose

ABCD

is a quadrilateral for which there is exactly one rotation, through an angle larger than

0\degree

and less than

360\degree

, which maps it to itself. Further, no reflections map

ABCD

to itself. What shape is

ABCD

?

The pickleball team paints a quadrilateral banner

ABCD

near the courts and a rotated copy

A'B'C'D'

near the pro shop. On the original banner,

AB = 19\text{ feet}

and

BC = 14\text{ feet}

. On the rotated banner,

C'D' = 16\text{ feet}

and

A'D' = 18\text{ feet}

.
How many feet of paint outline the perimeter of banner

ABCD

?

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